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
In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechan...In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechanics） with a macroscopic model （continuum mechanics）. We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.展开更多
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.
文摘In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechanics） with a macroscopic model （continuum mechanics）. We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.
