In this mini-review we summarize the progress of Lattice Boltzmann （LB） modeling and simulating compressible flows in our group in recent years. Main contents include （i） Single-Relaxation-Time （SRT） LB model su...In this mini-review we summarize the progress of Lattice Boltzmann （LB） modeling and simulating compressible flows in our group in recent years. Main contents include （i） Single-Relaxation-Time （SRT） LB model supplemented by additional viscosity, （ii） Multiple-Relaxation-Time （MRT） LB model, and （iii） LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model sup- plemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross Krook （LBGK）. So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a com- pletely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.展开更多
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen t...We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.展开更多
In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = ...In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.展开更多
In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves...In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L2 stable and the order of error estimates in the given norm is O（h｜logh｜^1/2）. Numerical experiments show the efficiency and accuracy of the method.展开更多
文摘In this mini-review we summarize the progress of Lattice Boltzmann （LB） modeling and simulating compressible flows in our group in recent years. Main contents include （i） Single-Relaxation-Time （SRT） LB model supplemented by additional viscosity, （ii） Multiple-Relaxation-Time （MRT） LB model, and （iii） LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model sup- plemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross Krook （LBGK）. So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a com- pletely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.
文摘We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
文摘In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.
基金Supported by the National Natural Science Foundation of China(Grant No.11171038)Youth Foundation of Tianyuan Mathematics(Grant No.11126279)+1 种基金The Science Foundation of China Academy of Engineering Physics(Grant No.2013A0202011)Defense Industrial Technology Development Program(Grant No.B1520133015)
文摘In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L2 stable and the order of error estimates in the given norm is O（h｜logh｜^1/2）. Numerical experiments show the efficiency and accuracy of the method.
