Accurate numerical discretizations of non-conservative hyperbolic systems

Ulrik Skre Fjordholm; Siddhartha Mishra

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2012)

  • Volume: 46, Issue: 1, page 187-206
  • ISSN: 0764-583X

Abstract

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We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating the robustness of this approach are presented.

How to cite

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Fjordholm, Ulrik Skre, and Mishra, Siddhartha. "Accurate numerical discretizations of non-conservative hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.1 (2012): 187-206. <http://eudml.org/doc/273098>.

@article{Fjordholm2012,
abstract = {We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating the robustness of this approach are presented.},
author = {Fjordholm, Ulrik Skre, Mishra, Siddhartha},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {non-conservative products; numerical schemes; non-conservative hyperbolic systems; entropy conservative discretizations; Lagrangian gas dynamics; isothermal Euler equations; numerical experiments},
language = {eng},
number = {1},
pages = {187-206},
publisher = {EDP-Sciences},
title = {Accurate numerical discretizations of non-conservative hyperbolic systems},
url = {http://eudml.org/doc/273098},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Fjordholm, Ulrik Skre
AU - Mishra, Siddhartha
TI - Accurate numerical discretizations of non-conservative hyperbolic systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 1
SP - 187
EP - 206
AB - We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating the robustness of this approach are presented.
LA - eng
KW - non-conservative products; numerical schemes; non-conservative hyperbolic systems; entropy conservative discretizations; Lagrangian gas dynamics; isothermal Euler equations; numerical experiments
UR - http://eudml.org/doc/273098
ER -

References

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