期刊
出版社
EDP SCIENCES S A
DOI: 10.1051/m2an:2002019
关键词
Saint-Venant system; shallow water equations; high-order central-upwind schemes; balance laws; conservation laws; source terms
资金
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [820817] Funding Source: National Science Foundation
We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes for systems of hyperbolic conservation laws to balance laws. Special attention is paid to the discretization of the source term such as to preserve stationary steady-state solutions. We also prove that the second-order version of our schemes preserves the nonnegativity of the height of the water. This important feature allows one to compute solutions for problems that include dry areas.
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