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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 35.4 (2010): 631-645. <http://eudml.org/doc/197530>.

@article{Jin2010,

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},

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

language = {eng},

month = {3},

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/197530},

volume = {35},

year = {2010},

}

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

DA - 2010/3//

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.; steady state solution; shock capturing methods; Godunov or Roe-type upwind methods

UR - http://eudml.org/doc/197530

ER -

## References

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