## Upwind methods for hyperbolic conservation laws with source terms.(English)Zbl 0816.76052

From the summary: The paper deals with the extension of some upwind schemes to hyperbolic systems of conservation laws with source term. More precisely, we give methods to get natural upwind discretizations of the source term when the flux is approximated by using flux-difference or flux-splitting techniques. In particular, the $$Q$$-schemes of Roe and van Leer and the flux-splitting techniques of Steger-Warming and Vijayasundaram are considered. Numerical results for a scalar advection equation with nonlinear source and for the one-dimensional shallow water equations are presented.

### MSC:

 76M20 Finite difference methods applied to problems in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35L65 Hyperbolic conservation laws

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### References:

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