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

Shi Jin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Jin, 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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Citations in EuDML Documents

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  1. Emmanuel Audusse, Marie-Odile Bristeau, Transport of pollutant in shallow water : a two time steps kinetic method
  2. Emmanuel Audusse, Marie-Odile Bristeau, Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method
  3. Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova, Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
  4. Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto, An entropy-correction free solver for non-homogeneous shallow water equations
  5. Stefania Ferrari, Fausto Saleri, A new two-dimensional shallow water model including pressure effects and slow varying bottom topography
  6. Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova, Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
  7. Stefania Ferrari, Fausto Saleri, A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography
  8. Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto, An entropy-correction free solver for non-homogeneous shallow water equations
  9. Alexander Kurganov, Doron Levy, Central-upwind schemes for the Saint-Venant system
  10. Alexander Kurganov, Doron Levy, Central-Upwind Schemes for the Saint-Venant System

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