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.

## 2017 |

Krüger, Timm; Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus The lattice Boltzmann method: Principles and practice Book Springer International Publishing, 2017, ISBN: 978-3-319-44647-9 / 978-3-319-44649-3. BibTeX | Tags: lattice boltzmann | Links: @book{kruger_lattice_2017, title = {The lattice Boltzmann method: Principles and practice}, author = {Timm Krüger and Halim Kusumaatmaja and Alexandr Kuzmin and Orest Shardt and Goncalo Silva and Erlend Magnus Viggen}, url = {http://link.springer.com/10.1007/978-3-319-44649-3, Download through SpringerLink http://www.springer.com/gp/book/9783319446479, Springer book page https://github.com/lbm-principles-practice/errata/blob/master/errata.pdf, Book errata }, doi = {10.1007/978-3-319-44649-3}, isbn = {978-3-319-44647-9 / 978-3-319-44649-3}, year = {2017}, date = {2017-01-01}, urldate = {2017-10-11}, publisher = {Springer International Publishing}, series = {Graduate Texts in Physics}, keywords = {lattice boltzmann}, pubstate = {published}, tppubtype = {book} } |

## 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 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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