Finite difference methods for problems of continuum mechanics on triangular and tetrahedral grids. (Russian. English summary) Zbl 1109.76339

Popov, I. V.; Polyakov, S. V.; Karamzin, Yu. N.

Mat. Model. 15, No. 11, 3-12 (2003).

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.

Reviewer: Sergei Georgievich Zhuravlev (Moskva)

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

Keywords:

continuum mechanics; hyperbolic equations; numerical approximation of solutions; finite difference scheme; grid methods