Volume 11, Issue 3
High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form

J. Koellermeier & M.J. Castro

East Asian J. Appl. Math., 11 (2021), pp. 435-467.

Published online: 2021-05

Export citation
  • 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.

  • Keywords

Hyperbolic moment model, non-conservative, high-order scheme.

  • AMS Subject Headings

65M08, 76P05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-11-435, author = {J. and Koellermeier and and 16209 and and J. Koellermeier and M.J. and Castro and and 16210 and and M.J. Castro}, title = {High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090920.130121}, url = {http://global-sci.org/intro/article_detail/eajam/19136.html} }
TY - JOUR T1 - High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form AU - Koellermeier , J. AU - Castro , M.J. JO - East Asian Journal on Applied Mathematics VL - 3 SP - 435 EP - 467 PY - 2021 DA - 2021/05 SN - 11 DO - http://doi.org/10.4208/eajam.090920.130121 UR - https://global-sci.org/intro/article_detail/eajam/19136.html KW - Hyperbolic moment model, non-conservative, high-order scheme. AB -

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.

J. Koellermeier & M.J. Castro. (2021). High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form. East Asian Journal on Applied Mathematics. 11 (3). 435-467. doi:10.4208/eajam.090920.130121
Copy to clipboard
The citation has been copied to your clipboard