Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy amo...Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions 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 edgemidpoint 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 conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical 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 nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.展开更多
基金This work was partially supported by the National Natural Science Foundation of China(No.11871009)Postdoctoral Research Foundation of China(No.BX20190013).
文摘Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions 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 edgemidpoint 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 conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical 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 nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.
