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Monotone Finite Volume Method on General Meshes

In: Parallel Finite Volume Computation on General Meshes

Author

Listed:
  • Yuri Vassilevski

    (Moscow Institute of Physics and Technology and Sechenov University , Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences and)

  • Kirill Terekhov

    (Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences)

  • Kirill Nikitin

    (Moscow State University, Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences and)

  • Ivan Kapyrin

    (Marchuk Institute of Numerical Mathematics and Nuclear Safety Institute of the Russian Academy of Sciences)

Abstract

Cell-centered finite volume (FV) discretizations are appealing for the approximate solution of boundary value problems since they are locally conservative and applicable to general meshes, i.e., to meshes with general polyhedral cells. In this chapter, we introduce nonlinear flux discretizations which result in monotone FV schemes at the cost of scheme nonlinearity, even if it is applied to a linear partial differential equation (PDE) such as diffusion and convection-diffusion equations. Also, we give two examples of linear two-point flux vector discretization of the diffusion equation in the mixed formulation and the Navier-Stokes equations. Such flux vector discretizations are stable in spite of degrees of freedom collocated at cell centers, are applicable to systems of PDEs, and demonstrate monotone numerical solutions.

Suggested Citation

  • Yuri Vassilevski & Kirill Terekhov & Kirill Nikitin & Ivan Kapyrin, 2020. "Monotone Finite Volume Method on General Meshes," Springer Books, in: Parallel Finite Volume Computation on General Meshes, chapter 0, pages 5-38, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-47232-0_2
    DOI: 10.1007/978-3-030-47232-0_2
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