Monotone finite point method for non-equilibrium radiation diffusion equations

Huang, Zhongyi; Li, Ye

doi:10.1007/s10543-015-0573-x

Cited by 10 publications

(2 citation statements)

References 25 publications

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“…However, these methods only can be used for the meshes with geometric restrictions. In [17], the authors propose a positivity-preserving finite point method for the nonequilibrium radiation diffusion equations. However, this method is not conservative, and it can only be used for the uniform mesh.…”

Section: Introductionmentioning

confidence: 99%

A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes

Yang

Peng

Gao

2022

Entropy

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In this paper, we propose a new positivity-preserving finite volume scheme with fixed stencils for the nonequilibrium radiation diffusion equations on distorted meshes. This scheme is used to simulate the equations on meshes with both the cell-centered and cell-vertex unknowns. The cell-centered unknowns are the primary unknowns, and the element vertex unknowns are taken as the auxiliary unknowns, which can be calculated by interpolation algorithm. With the nonlinear two-point flux approximation, the interpolation algorithm is not required to be positivity-preserving. Besides, the scheme has a fixed stencil and is locally conservative. The Anderson acceleration is used for the Picard method to solve the nonlinear systems efficiently. Several numerical results are also given to illustrate the efficiency and strong positivity-preserving quality of the scheme.

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Section: Introductionmentioning

confidence: 99%

A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes

Yang

Peng

Gao

2022

Entropy

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“…In [51], the authors designed two finite volume element schemes and proved that one of them is monotonic under some geometric conditions and another is monotonic under some repairing techniques. In [12], a monotone tailored finite point method was suggested for solving the non-equilibrium radiation diffusion equations. Recently, a moving mesh finite difference method was proposed in [44].…”

Section: Introductionmentioning

confidence: 99%

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

sci¹

2020

NMTMA

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Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons, ions and photons. In this paper, we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes. The vertex unknowns are treated as primary ones for which the finite volume equations are constructed. The edge-midpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns, which makes the final scheme a pure vertex-centered one. By comparison, most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal. Here, the co-normal decomposition is not convex in general, leading to a fixed stencil of the flux approximation and avoiding a certain search algorithm on complex grids. Moreover, the new scheme effectively alleviates the numerical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations. Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids. For the problem without analytic solution, the contours of the numerical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.

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Vertex-Centered Linearity-Preserving Schemes for Nonlinear Parabolic Problems on Polygonal Grids

2016

J Sci Comput

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Monotone finite point method for non-equilibrium radiation diffusion equations

Cited by 10 publications

References 25 publications

A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes

A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

Vertex-Centered Linearity-Preserving Schemes for Nonlinear Parabolic Problems on Polygonal Grids

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