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

Author

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  • Li, Ran
  • Zhou, Zhongguo
  • Li, Lin
  • Wang, Yan
  • Pan, Hao
  • Dong, Ruiqi
  • Zhou, Jing

Abstract

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.

Suggested Citation

  • Li, Ran & Zhou, Zhongguo & Li, Lin & Wang, Yan & Pan, Hao & Dong, Ruiqi & Zhou, Jing, 2020. "The mass-preserving domain decomposition scheme for solving three-dimensional convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 527-555.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:527-555
    DOI: 10.1016/j.matcom.2020.05.004
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    1. Zhou, Zhongguo & Liang, Dong & Wong, Yaushu, 2018. "The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 882-902.
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