The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredient...The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.展开更多
The DDFV(Discrete Duality Finite Volume)method is a finite volume scheme mainly dedicated to diffusion problems,with some outstanding properties.This scheme has been found to be one of the most accurate finite volume ...The DDFV(Discrete Duality Finite Volume)method is a finite volume scheme mainly dedicated to diffusion problems,with some outstanding properties.This scheme has been found to be one of the most accurate finite volume methods for diffusion problems.In the present paper,we propose a new monotonic extension of DDFV,which can handle discontinuous tensorial diffusion coefficient.Moreover,we compare its performance to a diamond type method with an original interpolation method relying on polynomial reconstructions.Monotonicity is achieved by adapting the method of Gao et al[A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes]to our schemes.Such a technique does not require the positiveness of the secondary unknowns.We show that the two new methods are second-order accurate and are indeed monotonic on some challenging benchmarks as a Fokker-Planck problem.展开更多
文摘The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.
文摘The DDFV(Discrete Duality Finite Volume)method is a finite volume scheme mainly dedicated to diffusion problems,with some outstanding properties.This scheme has been found to be one of the most accurate finite volume methods for diffusion problems.In the present paper,we propose a new monotonic extension of DDFV,which can handle discontinuous tensorial diffusion coefficient.Moreover,we compare its performance to a diamond type method with an original interpolation method relying on polynomial reconstructions.Monotonicity is achieved by adapting the method of Gao et al[A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes]to our schemes.Such a technique does not require the positiveness of the secondary unknowns.We show that the two new methods are second-order accurate and are indeed monotonic on some challenging benchmarks as a Fokker-Planck problem.
