The mass-preserving domain decomposition scheme for solving three-dimensional convection-diffusion equations

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 L2-norm with the restriction on the mesh step h=γ(Δt)2∕3. We give the error estimates and obtain the optimal convergence. Numerical experiments are presented to illustrate convergence and conservation.

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