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A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes
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A. A. Danilov
Published/Copyright:
June 10, 2009
Abstract
We have developed a new monotone cell-centered finite volume method for the discretization of diffusion equations on conformal polyhedral meshes. The proposed method is based on a nonlinear two-point flux approximation. For problems with smooth diffusion tensors and Dirichlet boundary conditions the method is interpolation-free. An adaptive interpolation is applied on faces where diffusion tensor jumps or Neumann boundary conditions are imposed. The interpolation is based on physical relationships such as continuity of the diffusion flux. The second-order convergence rate is verified with numerical experiments.
Published Online: 2009-06-10
Published in Print: 2009-May
© de Gruyter 2009
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Articles in the same Issue
- Numerical study of stability and transient phenomena of Poiseuille flows in ducts of square cross-sections
- A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes
- A finite-difference representation of the Coriolis force in numerical models of Godunov type for rotating shallow water flows
- Recurrent partial averaging in the theory of weighted Monte Carlo methods
- Spectral numerical models of fractional Brownian motion
- Approximate solution of integral equations with kernels of the form K(x – t) based on a special basis of trigonometric functions
