The mass-preserving domain decomposition scheme for solving three-dimensional convection-diffusion equations. (English) Zbl 1510.65198
Summary: In this paper, by combining the operator splitting and second order modified upwind technique, the mass-preserving domain decomposition method for solving time-dependent three dimensional convection-diffusion equations is analyzed. A three steps (\(x\)-direction, \(y\)-direction and \(z\)-direction) method is used to compute the solutions over each non-overlapping sub-domains at each time interval. The intermediate fluxes on the interfaces of sub-domains are firstly computed by the modified semi-implicit flux schemes. Then, the solutions and fluxes in the interiors of sub-domains are computed by the modified-upwind splitting implicit solution and flux coupled schemes. By rigorous mathematical analysis, we proved that our scheme is stable in discrete \(L^2\)-norm with the restriction on the mesh step \(h = \gamma ( \Delta t )^{2/3}\). We give the error estimates and obtain the optimal convergence. Numerical experiments are presented to illustrate convergence and conservation.
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 |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 76R05 | Forced convection |
Keywords:
three-dimensional convection-diffusion equations; mass-preserving; domain decomposition; modified-upwind; convergenceReferences:
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