Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diff...Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.展开更多
In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-des...In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-designs yield six infinite families of directed strongly regular graphs.展开更多
Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent b...Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions,which involve gradients evaluated at the boundaries,are implemented locally.A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated.Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence.The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11101407)the Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)
文摘Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.
基金Supported by National Natural Science Foundation of China(Grant No.61370187)
文摘In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-designs yield six infinite families of directed strongly regular graphs.
文摘Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions,which involve gradients evaluated at the boundaries,are implemented locally.A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated.Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence.The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.
