期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 26, 期 6, 页码 2079-2101出版社
SIAM PUBLICATIONS
DOI: 10.1137/040605825
关键词
shallow water equations; bottom topography; well-balanced schemes
We propose two simple well-balanced methods for hyperbolic systems with geometrical source terms having concentrations. Physical problems under consideration include the shallow water equations with topography and the quasi-one-dimensional isothermal nozzle flows. These two methods use the numerical fluxes already obtained from the corresponding homogeneous systems in the source terms, and one needs only a black-box (approximate) Riemann solver for the homogeneous system. Compared with our previous method developed in [S. Jin and X. Wen, J. Comput. Math., 22 (2004), pp. 230-249], these methods avoid the Newton iterations in the evaluation of the source term. Numerical experiments demonstrate that both methods give good numerical approximations to the subcritical and supercritical flows. With a transonic. x, both methods also capture with a high resolution the transonic flows over the concentration. These methods are applicable to both unsteady and steady state computations.
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