# A steady-state capturing method for hyperbolic systems with geometrical source terms

- Volume: 35, Issue: 4, page 631-645
- ISSN: 0764-583X

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topJin, Shi. "A steady-state capturing method for hyperbolic systems with geometrical source terms." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 631-645. <http://eudml.org/doc/194066>.

@article{Jin2001,

abstract = {We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar conservation laws and the one dimensional shallow water equations show much better resolution of the steady state than the conventional method, with almost no new numerical complexity.},

author = {Jin, Shi},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {hyperbolic systems; source terms; steady state solution; shallow water equations; shock capturing methods; Godunov or Roe-type upwind methods},

language = {eng},

number = {4},

pages = {631-645},

publisher = {EDP-Sciences},

title = {A steady-state capturing method for hyperbolic systems with geometrical source terms},

url = {http://eudml.org/doc/194066},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Jin, Shi

TI - A steady-state capturing method for hyperbolic systems with geometrical source terms

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 4

SP - 631

EP - 645

AB - We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar conservation laws and the one dimensional shallow water equations show much better resolution of the steady state than the conventional method, with almost no new numerical complexity.

LA - eng

KW - hyperbolic systems; source terms; steady state solution; shallow water equations; shock capturing methods; Godunov or Roe-type upwind methods

UR - http://eudml.org/doc/194066

ER -

## References

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