Year: 2021
Author: J. Koellermeier, M.J. Castro
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 435–467
Abstract
In this paper the first dedicated study on high-order non-conservative numerical schemes for hyperbolic moment models is presented. The implementation uses a new formulation that allows for explicit evaluation of the model while satisfying conservation of mass, momentum, and energy. The high-order numerical schemes use a path-conservative treatment of the non-conservative terms and a new consistent evaluation of the eigenvalues. The numerical results of two initial value problems, one stationary test case and a boundary value problem, yield stable and accurate solutions with convergence towards the reference solution despite the presence of a non-conservative term. A large speedup or accuracy gain in comparison to existing first-order codes could be demonstrated.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.090920.130121
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 435–467
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Hyperbolic moment model non-conservative high-order scheme.
Author Details
-
Entropy bounds for the space–time discontinuous Galerkin finite element moment method applied to the BGK–Boltzmann equation
Abdelmalik, M.R.A. | van der Woude, D.A.M. | van Brummelen, E.H.Computer Methods in Applied Mechanics and Engineering, Vol. 398 (2022), Iss. P.115162
https://doi.org/10.1016/j.cma.2022.115162 [Citations: 1] -
Hierarchical micro-macro acceleration for moment models of kinetic equations
Koellermeier, Julian | Vandecasteele, HannesJournal of Computational Physics, Vol. 488 (2023), Iss. P.112194
https://doi.org/10.1016/j.jcp.2023.112194 [Citations: 1] -
Projective Integration for Hyperbolic Shallow Water Moment Equations
Amrita, Amrita | Koellermeier, JulianAxioms, Vol. 11 (2022), Iss. 5 P.235
https://doi.org/10.3390/axioms11050235 [Citations: 2] -
Spatially Adaptive Projective Integration Schemes For Stiff Hyperbolic Balance Laws With Spectral Gaps
Koellermeier, Julian | Samaey, GiovanniThe SMAI Journal of computational mathematics, Vol. 8 (2022), Iss. P.295
https://doi.org/10.5802/smai-jcm.88 [Citations: 1] -
Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation
Koellermeier, Julian | Krah, Philipp | Kusch, JonasAdvances in Computational Mathematics, Vol. 50 (2024), Iss. 4
https://doi.org/10.1007/s10444-024-10175-y [Citations: 2] -
Positivity-Preserving Lax–Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models
Johnson, Erica R. | Rossmanith, James A. | Vaughan, ChristineJournal of Scientific Computing, Vol. 95 (2023), Iss. 1
https://doi.org/10.1007/s10915-023-02117-5 [Citations: 0] -
Hyperbolic Machine Learning Moment Closures for the BGK Equations
Christlieb, Andrew J. | Ding, Mingchang | Huang, Juntao | Krupansky, Nicholas A.Multiscale Modeling & Simulation, Vol. 23 (2025), Iss. 1 P.187
https://doi.org/10.1137/24M1629377 [Citations: 0]