Dr. Qiannan Dong, (ICMSEC, AMSS)

An unconditionally stable and linearity-preserving nine-point scheme for anisotorpic diffusion problems

12 月 22 日（周三） 下午 16:00-17:00

 The traditional cell-centered nine-point finite volume scheme is often applied in the process of radiation hydrodynamics, such as LARED-I and MARED. On a structural quadrilateral mesh, the scheme has a nine-point local stencil involving five cell-centered unknowns and four vertex-centered unknowns. Usually, the vertex unknowns are regarded as auxiliary ones, who can be eliminated or expressed as a combination of cell-centered unknowns through a certain interpolation method. However, the accuracy may be losed on some distorted meshes if the interpolation method is not appropriate. On the other hand, it’s usually difficult to provide reliable theoretical analysis due to its asymmetry. In this paper we use the dual mesh to construct an unconditional stable and linearity-preserving nine-point scheme for diffusion problems on general polygon meshes. This scheme maintains the advantages of the original nine-point scheme and at the same time has a certain stable convergence result. 

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