You can find a searchable list of my publications below. My Google Scholar profile contains an up-to-date overview of my citations. I also have a ResearchGate profile with most of my full-texts.

I am a strong proponent of Open Access, especially after having spent more than four years as a researcher at an institution with a very limited number of journal subscriptions. For each entry below where I am legally allowed to share a full-text, you can find it as the first link of the entry.

## 2020 |

Viggen, Erlend Magnus; Merciu, Ioan Alexandru; Løvstakken, Lasse; Måsøy, Svein-Erik Automatic interpretation of cement evaluation logs from cased boreholes using supervised deep neural networks Journal Article Journal of Petroleum Science and Engineering, 195 , pp. 17, 2020, ISSN: 0920-4105. Abstract | BibTeX | Tags: acoustics, machine learning, well logging | Links: @article{viggen_automatic_2020, title = {Automatic interpretation of cement evaluation logs from cased boreholes using supervised deep neural networks}, author = {Erlend Magnus Viggen and Ioan Alexandru Merciu and Lasse Løvstakken and Svein-Erik Måsøy}, url = {https://www.sciencedirect.com/science/article/pii/S0920410520306100}, doi = {10.1016/j.petrol.2020.107539}, issn = {0920-4105}, year = {2020}, date = {2020-12-01}, journal = {Journal of Petroleum Science and Engineering}, volume = {195}, pages = {17}, abstract = {The integrity of cement in cased boreholes is typically evaluated using well logging. However, well logging results are complex and can be ambiguous, and decisions associated with significant risks may be taken based on their interpretation. Cement evaluation logs must therefore be interpreted by trained professionals. To aid these interpreters, we propose a system for automatically interpreting cement evaluation logs, which they can use as a basis for their own interpretation. This system is based on deep convolutional neural networks, which we train in a supervised manner using a dataset of around 60 km of interpreted well log data. Thus, the networks learn the connections between data and interpretations during training. More specifically, the task of the networks is to classify the bond quality (among 6 ordinal classes) and the hydraulic isolation (2 classes) in each 1 m depth segment of each well based on the surrounding 13 m of well log data. We quantify the networks' performance by comparing over all segments how well the networks' interpretations of unseen data match the reference interpretations. For bond quality, the networks’ interpretation exactly matches the reference 51.6% of the time and is off by no more than one class 88.5% of the time. For hydraulic isolation, the interpretations match the reference 86.7% of the time. For comparison, a random-guess baseline gives matches of 16.7%, 44.4%, and 50%, respectively. We also compare with how well human reinterpretations of the log data match the reference interpretations, finding that the networks match the reference somewhat better. This may be linked to the networks learning and sharing the biases of the team behind the reference interpretations. An analysis of the results indicates that the subjectivity inherent in the interpretation process (and thereby in the reference interpretations we used for training and testing) is the main reason why we were not able to achieve an even better match between the networks and the reference.}, keywords = {acoustics, machine learning, well logging}, pubstate = {published}, tppubtype = {article} } The integrity of cement in cased boreholes is typically evaluated using well logging. However, well logging results are complex and can be ambiguous, and decisions associated with significant risks may be taken based on their interpretation. Cement evaluation logs must therefore be interpreted by trained professionals. To aid these interpreters, we propose a system for automatically interpreting cement evaluation logs, which they can use as a basis for their own interpretation. This system is based on deep convolutional neural networks, which we train in a supervised manner using a dataset of around 60 km of interpreted well log data. Thus, the networks learn the connections between data and interpretations during training. More specifically, the task of the networks is to classify the bond quality (among 6 ordinal classes) and the hydraulic isolation (2 classes) in each 1 m depth segment of each well based on the surrounding 13 m of well log data. We quantify the networks' performance by comparing over all segments how well the networks' interpretations of unseen data match the reference interpretations. For bond quality, the networks’ interpretation exactly matches the reference 51.6% of the time and is off by no more than one class 88.5% of the time. For hydraulic isolation, the interpretations match the reference 86.7% of the time. For comparison, a random-guess baseline gives matches of 16.7%, 44.4%, and 50%, respectively. We also compare with how well human reinterpretations of the log data match the reference interpretations, finding that the networks match the reference somewhat better. This may be linked to the networks learning and sharing the biases of the team behind the reference interpretations. An analysis of the results indicates that the subjectivity inherent in the interpretation process (and thereby in the reference interpretations we used for training and testing) is the main reason why we were not able to achieve an even better match between the networks and the reference. |

Viggen, Erlend Magnus (Ed.) Proceedings of the 43rd Scandinavian Symposium on Physical Acoustics Book Norwegian Physical Society, 2020, ISBN: 978-82-8123-020-0. BibTeX | Tags: acoustics | Links: @book{viggen_proceedings_2020, title = {Proceedings of the 43rd Scandinavian Symposium on Physical Acoustics}, editor = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/341043518_Proceedings_of_the_43rd_Scandinavian_Symposium_on_Physical_Acoustics, Link to proceedings}, isbn = {978-82-8123-020-0}, year = {2020}, date = {2020-04-30}, publisher = {Norwegian Physical Society}, keywords = {acoustics}, pubstate = {published}, tppubtype = {book} } |

Viggen, Erlend Magnus; Hårstad, Erlend; Kvalsvik, Jørgen Proceedings of the 43rd Scandinavian Symposium on Physical Acoustics, Norwegian Physical Society, Geilo, Norway, 2020, ISBN: 978-82-8123-020-0. Abstract | BibTeX | Tags: acoustics, well logging | Links: @conference{viggen_getting_2020, title = {Getting started with acoustic well log data using the dlisio Python library on the Volve Data Village dataset}, author = {Erlend Magnus Viggen and Erlend Hårstad and Jørgen Kvalsvik}, editor = {Erlend Magnus Viggen and Lars Hoff}, url = {https://www.researchgate.net/publication/340645995_Getting_started_with_acoustic_well_log_data_using_the_dlisio_Python_library_on_the_Volve_Data_Village_dataset, Full-text on ResearchGate https://github.com/equinor/dlisio-notebooks/blob/master/acoustic.ipynb, Companion Jupyter Notebook}, isbn = {978-82-8123-020-0}, year = {2020}, date = {2020-04-15}, booktitle = {Proceedings of the 43rd Scandinavian Symposium on Physical Acoustics}, pages = {36}, publisher = {Norwegian Physical Society}, address = {Geilo, Norway}, abstract = {Three issues have long impeded academic research and teaching on well logging. First, real measured data has been hard to come by. This has now been alleviated by Equinor's 2018 release of the Volve Data Village dataset. Among its 5 TB of data, it contains 16.3 GB of various well log data, plots, and analyses. Second, no free and effective software tools to programmatically read DLIS files, one of the most common file formats for well log data today and by far the most common format in the Volve Data Village, have been available. This has now been remedied by the free and open-source Python library dlisio, first released by Equinor in 2018 and still under heavy development. Third, the data is often difficult to understand, as sufficient documentation is often not publicly available. As different tools measure, process, and store their data differently, different tools must be understood individually. This article aims to stimulate research into well logging, by showing how to use dlisio to investigate well log data from the Volve Data Village dataset. While the investigative methods used here can be adapted to other kinds of data, this article focuses on acoustic integrity logs. Specifically, we investigate data from a sonic tool (DSLT) and an ultrasonic tool (USIT), both extensively used in the dataset. In addition to identifying what the most fundamental pieces of data represent, we also show some simple examples of how this data can be reprocessed to find new results not provided in the well log file. We provide the code underlying this article in an accompanying Jupyter Notebook.}, keywords = {acoustics, well logging}, pubstate = {published}, tppubtype = {conference} } Three issues have long impeded academic research and teaching on well logging. First, real measured data has been hard to come by. This has now been alleviated by Equinor's 2018 release of the Volve Data Village dataset. Among its 5 TB of data, it contains 16.3 GB of various well log data, plots, and analyses. Second, no free and effective software tools to programmatically read DLIS files, one of the most common file formats for well log data today and by far the most common format in the Volve Data Village, have been available. This has now been remedied by the free and open-source Python library dlisio, first released by Equinor in 2018 and still under heavy development. Third, the data is often difficult to understand, as sufficient documentation is often not publicly available. As different tools measure, process, and store their data differently, different tools must be understood individually. This article aims to stimulate research into well logging, by showing how to use dlisio to investigate well log data from the Volve Data Village dataset. While the investigative methods used here can be adapted to other kinds of data, this article focuses on acoustic integrity logs. Specifically, we investigate data from a sonic tool (DSLT) and an ultrasonic tool (USIT), both extensively used in the dataset. In addition to identifying what the most fundamental pieces of data represent, we also show some simple examples of how this data can be reprocessed to find new results not provided in the well log file. We provide the code underlying this article in an accompanying Jupyter Notebook. |

## 2019 |

Viggen, Erlend Magnus; Hoff, Lars (Ed.) Proceedings of the 42nd Scandinavian Symposium on Physical Acoustics Book Norwegian Physical Society, 2019, ISBN: 978-82-8123-019-4. BibTeX | Tags: acoustics | Links: @book{viggen_proceedings_2019, title = {Proceedings of the 42nd Scandinavian Symposium on Physical Acoustics}, editor = {Erlend Magnus Viggen and Lars Hoff}, url = {https://arxiv.org/html/1904.12488, Link to proceedings}, isbn = {978-82-8123-019-4}, year = {2019}, date = {2019-05-23}, publisher = {Norwegian Physical Society}, keywords = {acoustics}, pubstate = {published}, tppubtype = {book} } |

## 2017 |

Viggen, Erlend Magnus; Johansen, Tonni Franke; Merciu, Ioan-Alexandru Simulation and inversion of ultrasonic pitch-catch through-tubing well logging with an array of receivers Journal Article NDT & E International, 85 , pp. 72–75, 2017, ISSN: 09638695. Abstract | BibTeX | Tags: acoustics, well logging | Links: @article{viggen_simulation_2017, title = {Simulation and inversion of ultrasonic pitch-catch through-tubing well logging with an array of receivers}, author = {Erlend Magnus Viggen and Tonni Franke Johansen and Ioan-Alexandru Merciu}, url = {https://erlend-viggen.no/wp-content/uploads/2018/04/viggen_simulation_2017_post-print.pdf, Full-text}, doi = {10.1016/j.ndteint.2016.10.008}, issn = {09638695}, year = {2017}, date = {2017-01-01}, urldate = {2017-10-11}, journal = {NDT & E International}, volume = {85}, pages = {72--75}, abstract = {Current methods for ultrasonic pitch-catch well logging use two receivers to log the bonded material outside a single casing. For two casings separated by a fluid, we find by simulation that increasing the number of receivers provides a better picture of the effect of the bonded material outside the second casing. Inverting simulated measurements with five receivers, using a simulated annealing algorithm and a simple forward model, we find for a subset of simulations that we can estimate the impedance of the material outside the outer casing.}, keywords = {acoustics, well logging}, pubstate = {published}, tppubtype = {article} } Current methods for ultrasonic pitch-catch well logging use two receivers to log the bonded material outside a single casing. For two casings separated by a fluid, we find by simulation that increasing the number of receivers provides a better picture of the effect of the bonded material outside the second casing. Inverting simulated measurements with five receivers, using a simulated annealing algorithm and a simple forward model, we find for a subset of simulations that we can estimate the impedance of the material outside the outer casing. |

## 2016 |

Viggen, Erlend Magnus; Johansen, Tonni Franke; Merciu, Ioan-Alexandru Simulation and modeling of ultrasonic pitch-catch through-tubing logging Journal Article Geophysics, 81 (4), pp. D383-D393, 2016. Abstract | BibTeX | Tags: acoustics, well logging | Links: @article{viggen_simulation_2016, title = {Simulation and modeling of ultrasonic pitch-catch through-tubing logging}, author = {Erlend Magnus Viggen and Tonni Franke Johansen and Ioan-Alexandru Merciu}, url = {https://erlend-viggen.no/wp-content/uploads/2018/04/viggen_simulation_2016.pdf, Full-text}, doi = {10.1190/geo2015-0251.1}, year = {2016}, date = {2016-07-01}, journal = {Geophysics}, volume = {81}, number = {4}, pages = {D383-D393}, abstract = {Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the sealing material and to determine the structural integrity status. Although ultrasonic pitch-catch logging in single-casing geometries has been widely studied and is commercially available, this is not the case for logging in double-casing geometries despite its increasing importance in plug and abandonment operations. It is therefore important to investigate whether existing logging tools can be used in such geometries. Using a finite-element model of a double-casing geometry with a two-receiver pitch-catch setup, we have simulated through-tubing logging, with fluid between the two casings. We found that there appears a cascade of leaky Lamb wave packets on both casings, linked by leaked wavefronts. By varying the geometry and materials in the model, we have examined the effect on the pulse received from the second wave packet on the inner casing, sometimes known as the third interface echo. The amplitude of this pulse was found to contain information on the bonded material in the outer annulus. Much stronger amplitude variations were found with two equally thick casings than with a significant thickness difference; relative thickness differences of up to one-third were simulated. Finally, we have developed a simple mathematical model of the wave packets’ time evolution to encapsulate and validate our understanding of the wave packet cascade. This model shows a more complex time evolution in the later wave packets than the exponentially attenuated primary packet, which is currently used for single-casing logging. This indicates that tools with more than two receivers, which could measure wave packets’ amplitude at more than two points along their time evolution, would be able to draw more information from these later packets. The model was validated against simulations, finding good agreement when the underlying assumptions of the model were satisfied.}, keywords = {acoustics, well logging}, pubstate = {published}, tppubtype = {article} } Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the sealing material and to determine the structural integrity status. Although ultrasonic pitch-catch logging in single-casing geometries has been widely studied and is commercially available, this is not the case for logging in double-casing geometries despite its increasing importance in plug and abandonment operations. It is therefore important to investigate whether existing logging tools can be used in such geometries. Using a finite-element model of a double-casing geometry with a two-receiver pitch-catch setup, we have simulated through-tubing logging, with fluid between the two casings. We found that there appears a cascade of leaky Lamb wave packets on both casings, linked by leaked wavefronts. By varying the geometry and materials in the model, we have examined the effect on the pulse received from the second wave packet on the inner casing, sometimes known as the third interface echo. The amplitude of this pulse was found to contain information on the bonded material in the outer annulus. Much stronger amplitude variations were found with two equally thick casings than with a significant thickness difference; relative thickness differences of up to one-third were simulated. Finally, we have developed a simple mathematical model of the wave packets’ time evolution to encapsulate and validate our understanding of the wave packet cascade. This model shows a more complex time evolution in the later wave packets than the exponentially attenuated primary packet, which is currently used for single-casing logging. This indicates that tools with more than two receivers, which could measure wave packets’ amplitude at more than two points along their time evolution, would be able to draw more information from these later packets. The model was validated against simulations, finding good agreement when the underlying assumptions of the model were satisfied. |

Viggen, Erlend Magnus; Kristiansen, Ulf R (Ed.) Proceedings of the 39th Scandinavian Symposium on Physical Acoustics Book 2016, ISBN: 978-82-8123-016-3. BibTeX | Tags: acoustics | Links: @book{viggen_proceedings_2016, title = {Proceedings of the 39th Scandinavian Symposium on Physical Acoustics}, editor = {Erlend Magnus Viggen and Ulf R Kristiansen}, url = {https://arxiv.org/html/1604.01763, Link to proceedings}, isbn = {978-82-8123-016-3}, year = {2016}, date = {2016-04-11}, keywords = {acoustics}, pubstate = {published}, tppubtype = {book} } |

Viggen, Erlend Magnus; Johansen, Tonni Franke; Merciu, Ioan-Alexandru Analysis of outer-casing echoes in simulations of ultrasonic pulse-echo through-tubing logging Journal Article Geophysics, 81 (6), pp. D679–D685, 2016, ISSN: 0016-8033, 1942-2156. Abstract | BibTeX | Tags: acoustics, well logging | Links: @article{viggen_analysis_2016, title = {Analysis of outer-casing echoes in simulations of ultrasonic pulse-echo through-tubing logging}, author = {Erlend Magnus Viggen and Tonni Franke Johansen and Ioan-Alexandru Merciu}, url = {https://erlend-viggen.no/wp-content/uploads/2018/04/viggen_analysis_2016.pdf, Full-text}, doi = {10.1190/geo2015-0376.1}, issn = {0016-8033, 1942-2156}, year = {2016}, date = {2016-01-01}, urldate = {2017-10-11}, journal = {Geophysics}, volume = {81}, number = {6}, pages = {D679--D685}, abstract = {Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the cement. Ultrasonic logging of single casings has been widely studied and is commercially available. However, ultrasonic logging in multiple-casing geometries is an unexplored topic despite its importance in plug and abandonment operations. Therefore, current logging technologies should be studied to evaluate whether they indicate the potential for multiple-casing logging. In this study, we used two finite-element models of pulse-echo logging. The first model represents logging in the transverse cross section of a double-casing well. The second model is a copy of the first, but with the outer casing and formation removed so that the pulse-echo transducer receives only a resonant first interface echo from the inner casing. By subtracting the received signals of the second model from those of the first, we can recover the third interface echo (TIE) signal representing the resonant reflection from the outer casing. This signal is used to study what information can, in principle, be drawn from TIEs in double-casing geometries, with the caveat that TIEs can only approximately be recovered in practical cases. We simulated variations of the material in the annulus beyond the outer casing, of the thickness of the outer casing, and of the eccentering of the outer casing. We have determined that the first two of these variations have only weak effects on the TIE, but that the eccentering of the outer casing can, in principle, be found using the TIE arrival time.}, keywords = {acoustics, well logging}, pubstate = {published}, tppubtype = {article} } Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the cement. Ultrasonic logging of single casings has been widely studied and is commercially available. However, ultrasonic logging in multiple-casing geometries is an unexplored topic despite its importance in plug and abandonment operations. Therefore, current logging technologies should be studied to evaluate whether they indicate the potential for multiple-casing logging. In this study, we used two finite-element models of pulse-echo logging. The first model represents logging in the transverse cross section of a double-casing well. The second model is a copy of the first, but with the outer casing and formation removed so that the pulse-echo transducer receives only a resonant first interface echo from the inner casing. By subtracting the received signals of the second model from those of the first, we can recover the third interface echo (TIE) signal representing the resonant reflection from the outer casing. This signal is used to study what information can, in principle, be drawn from TIEs in double-casing geometries, with the caveat that TIEs can only approximately be recovered in practical cases. We simulated variations of the material in the annulus beyond the outer casing, of the thickness of the outer casing, and of the eccentering of the outer casing. We have determined that the first two of these variations have only weak effects on the TIE, but that the eccentering of the outer casing can, in principle, be found using the TIE arrival time. |

## 2015 |

Viggen, Erlend Magnus; Solvang, Audun; Vennerød, Jakob; Olsen, Herold Development of an outdoor auralisation prototype with 3D sound reproduction Conference Proceedings of the 18th International Conference on Digital Audio Effects (DAFx-15), Trondheim, 2015. Abstract | BibTeX | Tags: acoustics, auralisation | Links: @conference{viggen_development_2015, title = {Development of an outdoor auralisation prototype with 3D sound reproduction}, author = {Erlend Magnus Viggen and Audun Solvang and Jakob Vennerød and Herold Olsen}, url = {https://www.researchgate.net/publication/285592626_Development_of_an_outdoor_auralisation_prototype_with_3D_sound_reproduction, Full-text on ResearchGate}, year = {2015}, date = {2015-12-01}, booktitle = {Proceedings of the 18th International Conference on Digital Audio Effects (DAFx-15)}, address = {Trondheim}, abstract = {Auralisation of outdoor sound has a strong potential for demonstrating the impact of different community noise scenarios. We describe here the development of an auralisation tool for outdoor noise such as traffic or industry. The tool calculates the sound propagation from source to listener using the Nord2000 model, and represents the sound field at the listener's position using spherical harmonics. Because of this spherical harmonics approach, the sound may be reproduced in various formats, such as headphones, stereo, or surround. Dynamic reproduction in headphones according to the listener's head orientation is also possible through the use of head tracking.}, keywords = {acoustics, auralisation}, pubstate = {published}, tppubtype = {conference} } Auralisation of outdoor sound has a strong potential for demonstrating the impact of different community noise scenarios. We describe here the development of an auralisation tool for outdoor noise such as traffic or industry. The tool calculates the sound propagation from source to listener using the Nord2000 model, and represents the sound field at the listener's position using spherical harmonics. Because of this spherical harmonics approach, the sound may be reproduced in various formats, such as headphones, stereo, or surround. Dynamic reproduction in headphones according to the listener's head orientation is also possible through the use of head tracking. |

## 2014 |

Viggen, Erlend Magnus The lattice Boltzmann method: Fundamentals and acoustics PhD Thesis Norwegian University of Science and Technology, 2014. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @phdthesis{viggen_lattice_2014, title = {The lattice Boltzmann method: Fundamentals and acoustics}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/263714289_The_lattice_Boltzmann_method_Fundamentals_and_acoustics, Full-text on ResearchGate}, year = {2014}, date = {2014-02-21}, address = {Trondheim}, school = {Norwegian University of Science and Technology}, abstract = {The lattice Boltzmann method has been widely used as a solver for incompressible flow, though it is not restricted to this application. More generally, it can be used as a compressible Navier-Stokes solver, albeit with a restriction that the Mach number is low. While that restriction may seem strict, it does not hinder the application of the method to the simulation of sound waves, for which the Mach numbers are generally very low. Even sound waves with strong nonlinear effects can be captured well. Despite this, the method has not been as widely used for problems where acoustic phenomena are involved as it has been for incompressible problems. The research presented this thesis goes into three different aspects of lattice Boltzmann acoustics. Firstly, linearisation analyses are used to derive and compare the sound propagation properties of the lattice Boltzmann equation and comparable fluid models for both free and forced waves. The propagation properties of the fully discrete lattice Boltzmann equation are shown to converge at second order towards those of the discrete-velocity Boltzmann equation, which itself predicts the same lowest-order absorption but different dispersion to the other fluid models. Secondly, it is shown how multipole sound sources can be created mesoscopically by adding a particle source term to the Boltzmann equation. This method is straightforwardly extended to the lattice Boltzmann method by discretisation. The results of lattice Boltzmann simulations of monopole, dipole, and quadrupole point sources are shown to agree very well with the combined predictions of this multipole method and the linearisation analysis. The exception to this agreement is the immediate vicinity of the point source, where the singularity in the analytical solution cannot be reproduced numerically. Thirdly, an extended lattice Boltzmann model is described. This model alters the equilibrium distribution to reproduce variable equations of state while remaining simple to implement and efficient to run. To compensate for an unphysical bulk viscosity, the extended model contains a bulk viscosity correction term. It is shown that all equilibrium distributions that allow variable equations of state must be identical for the one-dimensional D1Q3 velocity set. Using such a D1Q3 velocity set and an isentropic equation of state, both mechanisms of nonlinear acoustics are captured successfully in a simulation, improving on previous isothermal simulations where only one mechanism could be captured. In addition, the effect of molecular relaxation on sound propagation is simulated using a model equation of state. Though the particular implementation used is not completely stable, the results agree well with theory.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {phdthesis} } The lattice Boltzmann method has been widely used as a solver for incompressible flow, though it is not restricted to this application. More generally, it can be used as a compressible Navier-Stokes solver, albeit with a restriction that the Mach number is low. While that restriction may seem strict, it does not hinder the application of the method to the simulation of sound waves, for which the Mach numbers are generally very low. Even sound waves with strong nonlinear effects can be captured well. Despite this, the method has not been as widely used for problems where acoustic phenomena are involved as it has been for incompressible problems. The research presented this thesis goes into three different aspects of lattice Boltzmann acoustics. Firstly, linearisation analyses are used to derive and compare the sound propagation properties of the lattice Boltzmann equation and comparable fluid models for both free and forced waves. The propagation properties of the fully discrete lattice Boltzmann equation are shown to converge at second order towards those of the discrete-velocity Boltzmann equation, which itself predicts the same lowest-order absorption but different dispersion to the other fluid models. Secondly, it is shown how multipole sound sources can be created mesoscopically by adding a particle source term to the Boltzmann equation. This method is straightforwardly extended to the lattice Boltzmann method by discretisation. The results of lattice Boltzmann simulations of monopole, dipole, and quadrupole point sources are shown to agree very well with the combined predictions of this multipole method and the linearisation analysis. The exception to this agreement is the immediate vicinity of the point source, where the singularity in the analytical solution cannot be reproduced numerically. Thirdly, an extended lattice Boltzmann model is described. This model alters the equilibrium distribution to reproduce variable equations of state while remaining simple to implement and efficient to run. To compensate for an unphysical bulk viscosity, the extended model contains a bulk viscosity correction term. It is shown that all equilibrium distributions that allow variable equations of state must be identical for the one-dimensional D1Q3 velocity set. Using such a D1Q3 velocity set and an isentropic equation of state, both mechanisms of nonlinear acoustics are captured successfully in a simulation, improving on previous isothermal simulations where only one mechanism could be captured. In addition, the effect of molecular relaxation on sound propagation is simulated using a model equation of state. Though the particular implementation used is not completely stable, the results agree well with theory. |

Viggen, Erlend Magnus Acoustic equations of state for simple lattice Boltzmann velocity sets Journal Article Physical Review E, 90 , pp. 013310, 2014, ISSN: 1539-3755, 1550-2376. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @article{viggen_acoustic_2014, title = {Acoustic equations of state for simple lattice Boltzmann velocity sets}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/264397832_Acoustic_equations_of_state_for_simple_lattice_Boltzmann_velocity_sets, Full-text on ResearchGate}, doi = {10.1103/PhysRevE.90.013310}, issn = {1539-3755, 1550-2376}, year = {2014}, date = {2014-01-01}, urldate = {2018-04-04}, journal = {Physical Review E}, volume = {90}, pages = {013310}, abstract = {The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξiα ∈ −1,0,1 for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {article} } The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξiα ∈ −1,0,1 for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics. |

## 2013 |

Viggen, Erlend Magnus Sound propagation properties of the discrete-velocity Boltzmann equation Journal Article Communications in Computational Physics, 13 (3), pp. 671–684, 2013. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @article{viggen_sound_2013, title = {Sound propagation properties of the discrete-velocity Boltzmann equation}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/263714278_Sound_Propagation_Properties_of_the_Discrete-Velocity_Boltzmann_Equation, Full-text on ResearchGate}, doi = {10.4208/cicp.271011.020212s}, year = {2013}, date = {2013-03-01}, journal = {Communications in Computational Physics}, volume = {13}, number = {3}, pages = {671--684}, abstract = {As the numerical resolution is increased and the discretisation error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmann equation (DVBE). An expression for the propagation properties of plane sound waves is found for this equation. This expression is compared to similar ones from the Navier-Stokes and Burnett models, and is found to be closest to the latter. The anisotropy of sound propagation with the DVBE is examined using a two-dimensional velocity set. It is found that both the anisotropy and the deviation between the models is negligible if the Knudsen number is less than 1 by at least an order of magnitude.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {article} } As the numerical resolution is increased and the discretisation error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmann equation (DVBE). An expression for the propagation properties of plane sound waves is found for this equation. This expression is compared to similar ones from the Navier-Stokes and Burnett models, and is found to be closest to the latter. The anisotropy of sound propagation with the DVBE is examined using a two-dimensional velocity set. It is found that both the anisotropy and the deviation between the models is negligible if the Knudsen number is less than 1 by at least an order of magnitude. |

Viggen, Erlend Magnus Acoustic multipole sources from the Boltzmann equation Conference Proceedings of the 36th Scandinavian Symposium on Physical Acoustics, Norwegian Physical Society, Geilo, Norway, 2013. Abstract | BibTeX | Tags: acoustics | Links: @conference{viggen_acoustic_2013b, title = {Acoustic multipole sources from the Boltzmann equation}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/235633945_Acoustic_multipole_sources_from_the_Boltzmann_equation, Full-text on ResearchGate}, year = {2013}, date = {2013-02-01}, booktitle = {Proceedings of the 36th Scandinavian Symposium on Physical Acoustics}, publisher = {Norwegian Physical Society}, address = {Geilo, Norway}, abstract = {By adding a particle source term in the Boltzmann equation of kinetic theory, it is possible to represent particles appearing and disappearing throughout the fluid with a specified distribution of particle velocities. By deriving the wave equation from this modified Boltzmann equation via the conservation equations of fluid mechanics, multipole source terms in the wave equation are found. These multipole source terms are given by the particle source term in the Boltzmann equation. To the Euler level in the momentum equation, a monopole and a dipole source term appear in the wave equation. To the Navier-Stokes level, a quadrupole term with negligible magnitude also appears.}, keywords = {acoustics}, pubstate = {published}, tppubtype = {conference} } By adding a particle source term in the Boltzmann equation of kinetic theory, it is possible to represent particles appearing and disappearing throughout the fluid with a specified distribution of particle velocities. By deriving the wave equation from this modified Boltzmann equation via the conservation equations of fluid mechanics, multipole source terms in the wave equation are found. These multipole source terms are given by the particle source term in the Boltzmann equation. To the Euler level in the momentum equation, a monopole and a dipole source term appear in the wave equation. To the Navier-Stokes level, a quadrupole term with negligible magnitude also appears. |

Viggen, Erlend Magnus Acoustic multipole sources for the lattice Boltzmann method Journal Article Physical Review E, 87 (2), pp. 023306, 2013. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @article{viggen_acoustic_2013, title = {Acoustic multipole sources for the lattice Boltzmann method}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/236051059_Acoustic_multipole_sources_for_the_lattice_Boltzmann_method, Full-text on ResearchGate}, doi = {10.1103/PhysRevE.87.023306}, year = {2013}, date = {2013-01-01}, journal = {Physical Review E}, volume = {87}, number = {2}, pages = {023306}, abstract = {By including an oscillating particle source term, acoustic multipole sources can be implemented in the lattice Boltzmann method. The effect of this source term on the macroscopic conservation equations is found using a Chapman-Enskog expansion. In a lattice with q particle velocities, the source term can be decomposed into q orthogonal multipoles. More complex sources may be formed by superposing these basic multipoles. Analytical solutions found from the macroscopic equations and an analytical lattice Boltzmann wavenumber are compared with inviscid multipole simulations, finding very good agreement except close to singularities in the analytical solutions. Unlike the BGK operator, the regularized collision operator is proven capable of accurately simulating two-dimensional acoustic generation and propagation at zero viscosity.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {article} } By including an oscillating particle source term, acoustic multipole sources can be implemented in the lattice Boltzmann method. The effect of this source term on the macroscopic conservation equations is found using a Chapman-Enskog expansion. In a lattice with q particle velocities, the source term can be decomposed into q orthogonal multipoles. More complex sources may be formed by superposing these basic multipoles. Analytical solutions found from the macroscopic equations and an analytical lattice Boltzmann wavenumber are compared with inviscid multipole simulations, finding very good agreement except close to singularities in the analytical solutions. Unlike the BGK operator, the regularized collision operator is proven capable of accurately simulating two-dimensional acoustic generation and propagation at zero viscosity. |

## 2011 |

Viggen, Erlend Magnus Viscously damped acoustic waves with the lattice Boltzmann method Journal Article Philosophical Transactions of the Royal Society A, 369 (1944), pp. 2246–2254, 2011. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @article{viggen_viscously_2011, title = {Viscously damped acoustic waves with the lattice Boltzmann method}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/51092609_Viscously_damped_acoustic_waves_with_the_lattice_Boltzmann_method, Full-text on ResearchGate}, doi = {10.1098/rsta.2011.0040}, year = {2011}, date = {2011-06-01}, journal = {Philosophical Transactions of the Royal Society A}, volume = {369}, number = {1944}, pages = {2246--2254}, abstract = {Acoustic wave propagation in lattice Boltzmann Bhatnagar-Gross-Krook simulations may be analysed using a linearization method. This method has been used in the past to study the propagation of waves that are viscously damped in time, and is here extended to also study waves that are viscously damped in space. Its validity is verified against simulations, and the results are compared with theoretical expressions. It is found in the infinite resolution limit k→0 that the absorption coefficients and phase differences between density and velocity waves match theoretical expressions for small values of ωτ(ν), the characteristic number for viscous acoustic damping. However, the phase velocities and amplitude ratios between the waves increase incorrectly with (ωτ(ν))(2), and agree with theory only in the inviscid limit k→0, ωτ(ν)→0. The actual behaviour of simulated plane waves in the infinite resolution limit is quantified.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {article} } Acoustic wave propagation in lattice Boltzmann Bhatnagar-Gross-Krook simulations may be analysed using a linearization method. This method has been used in the past to study the propagation of waves that are viscously damped in time, and is here extended to also study waves that are viscously damped in space. Its validity is verified against simulations, and the results are compared with theoretical expressions. It is found in the infinite resolution limit k→0 that the absorption coefficients and phase differences between density and velocity waves match theoretical expressions for small values of ωτ(ν), the characteristic number for viscous acoustic damping. However, the phase velocities and amplitude ratios between the waves increase incorrectly with (ωτ(ν))(2), and agree with theory only in the inviscid limit k→0, ωτ(ν)→0. The actual behaviour of simulated plane waves in the infinite resolution limit is quantified. |

## 2010 |

Viggen, Erlend Magnus The lattice Boltzmann method in acoustics Conference Proceedings of the 33rd Scandinavian Symposium on Physical Acoustics, Norwegian Physical Society, Geilo, Norway, 2010. Abstract | BibTeX | Tags: acoustics, lattice boltzmann | Links: @conference{viggen_lattice_2010, title = {The lattice Boltzmann method in acoustics}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/263739190_The_lattice_Boltzmann_method_in_acoustics, Full-text on ResearchGate}, year = {2010}, date = {2010-02-01}, booktitle = {Proceedings of the 33rd Scandinavian Symposium on Physical Acoustics}, publisher = {Norwegian Physical Society}, address = {Geilo, Norway}, abstract = {The lattice Boltzmann method, a method based in kinetic theory and used for simulating fluid behaviour, is presented with particular regard to usage in acoustics. A point source method of generating acoustic waves in the computational domain is presented, and simple simulation results with this method are analysed. The simulated waves' transient wavefronts in one dimension are shown to agree with analytical solutions from acoustic theory. The phase velocity and absorption coefficients of the waves and their deviations from theory are analysed. Finally, the physical time and space steps relating simulation units with physical units are discussed and shown to limit acoustic usage of the method to small scales in time and space.}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {conference} } The lattice Boltzmann method, a method based in kinetic theory and used for simulating fluid behaviour, is presented with particular regard to usage in acoustics. A point source method of generating acoustic waves in the computational domain is presented, and simple simulation results with this method are analysed. The simulated waves' transient wavefronts in one dimension are shown to agree with analytical solutions from acoustic theory. The phase velocity and absorption coefficients of the waves and their deviations from theory are analysed. Finally, the physical time and space steps relating simulation units with physical units are discussed and shown to limit acoustic usage of the method to small scales in time and space. |

## 2009 |

Viggen, Erlend Magnus The Lattice Boltzmann Method with Applications in Acoustics Masters Thesis Norwegian University of Science and Technology (NTNU), 2009. BibTeX | Tags: acoustics, lattice boltzmann | Links: @mastersthesis{viggen_lattice_2009, title = {The Lattice Boltzmann Method with Applications in Acoustics}, author = {Erlend Magnus Viggen}, url = {https://www.researchgate.net/publication/242162544_The_Lattice_Boltzmann_Method_with_Applications_in_Acoustics, Full-text on ResearchGate}, year = {2009}, date = {2009-07-01}, address = {Trondheim}, school = {Norwegian University of Science and Technology (NTNU)}, keywords = {acoustics, lattice boltzmann}, pubstate = {published}, tppubtype = {mastersthesis} } |

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