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.

中文翻译：

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求解三维对流-扩散方程的质量保持域分解方案

本文结合算子分裂和二阶修正迎风技术，分析了求解时变三维对流扩散方程的质量保持域分解方法。三个步骤（x 方向、y 方向和 z 方向）方法用于计算每个时间间隔的每个非重叠子域上的解决方案。子域界面上的中间通量首先通过改进的半隐式通量方案计算。然后，通过改进的迎风分裂隐式解和通量耦合方案计算子域内部的解和通量。通过严格的数学分析，我们证明了我们的方案在离散L2范数下是稳定的，并且网格步长h=γ(Δt)2∕3。我们给出误差估计并获得最优收敛。给出了数值实验来说明收敛和守恒。