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Discrete kinetic schemes for multidimensional systems of conservation laws. (English) Zbl 0964.65096
The authors propose a family of difference schemes for multidimensional systems of conservation laws. These schemes generalize the method of P. L. Bhatnagar, E. P. Gross, and M. Krook [Phys. Review, II. Ser. 94, 511-525 (1954; Zbl 0055.23609)], which uses ideas from kinetic theory to solve the equations of gas dynamics. Stability conditions are derived, and convergence is proved for scalar problems.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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