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Finite difference methods for problems of continuum mechanics on triangular and tetrahedral grids. (Russian. English summary) Zbl 1109.76339
Some approaches for the solution of modern problems of continuum mechanics by finite difference schemes are considered. One of the important procedure in such schemes is the decomposition of 2-D and 3-D multiply connected nonconvex domains in triangles and thetrahedra. Some new algorithms for the decomposition are proposed and then an original finite difference scheme with a high order of accuracy is used for the solution of the standard parabolic and transport problems.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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Full Text: MNR