Geodesic
A steady-state capturing method for hyperbolic systems with geometrical source terms
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 631-645

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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.

Classification : 35L65, 65M06, 76B15
Keywords: hyperbolic systems, source terms, steady state solution, shallow water equations, shock capturing methods 
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     author = {Jin, Shi},
     title = {A steady-state capturing method for hyperbolic systems with geometrical source terms},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {631--645},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1862872},
     zbl = {1001.35083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_631_0/}
}
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Jin, Shi. A steady-state capturing method for hyperbolic systems with geometrical source terms. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 631-645. http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_631_0/