In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale fin...In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier- Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with Re = 5000, 7500 and 10000. We present the numerical results as the time are sufficient long, so that the steady state numerical solutions can be obtained.展开更多
This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSA...This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based(CB)Godunov-type treatment of convective terms with PP methods.Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP(split)methods,thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible.Therefore,the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a)overcome the numerical stiffness of the classical AC approach at(very)low and moderate Reynolds numbers,b)incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods,and c)further improve the stability and efficiency of the AC method for steady and unsteady flow problems.The FSAC-PP method has also been coupled with a non-linear,full-multigrid and fullapproximation storage(FMG-FAS)technique to further increase the efficiency of the solution.For validating the proposed FSAC-PP method,computational examples are presented for benchmark problems.The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.展开更多
文摘In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier- Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with Re = 5000, 7500 and 10000. We present the numerical results as the time are sufficient long, so that the steady state numerical solutions can be obtained.
文摘This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based(CB)Godunov-type treatment of convective terms with PP methods.Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP(split)methods,thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible.Therefore,the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a)overcome the numerical stiffness of the classical AC approach at(very)low and moderate Reynolds numbers,b)incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods,and c)further improve the stability and efficiency of the AC method for steady and unsteady flow problems.The FSAC-PP method has also been coupled with a non-linear,full-multigrid and fullapproximation storage(FMG-FAS)technique to further increase the efficiency of the solution.For validating the proposed FSAC-PP method,computational examples are presented for benchmark problems.The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.
