In present paper,the mathematic background of intrusive polynomial chaos (IPC) method and coupling process with one dimension Euler equation were introduced. The IPC method was implemented for the 2D compressible stoc...In present paper,the mathematic background of intrusive polynomial chaos (IPC) method and coupling process with one dimension Euler equation were introduced. The IPC method was implemented for the 2D compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a lid driven cavity flow under the influence of uncertainties. The driven velocity and fluid viscosity were supposed respectively to be the uncertain variable which has Gaussian probability distribution. Based on the validation with benchmark results,discussions were mainly focused on the statistic properties of velocity distribution. The results indicated the effect of IPC method on the simulation of propagation of uncertainty in the flow field. For the simulated results of 2D cavity flow,influence of the driven velocity uncertainty is larger than that of viscosity.展开更多
By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improv...By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.展开更多
A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for-...A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.展开更多
Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move ...Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move at the same speed but in opposite directions so that symmetric flow patterns are generated. Similar to the Newtonian case, bifurcations occur as the aspect ratio decreases. Special to Bingham fluids, the non-Newtonian indicator, Bingham number B, also governs the bifurcation besides the bifurcation parameter A.展开更多
Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the sch...Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.90718025)the EU Six Frame Project(Grant No.AST5-CT-2006-030959)
文摘In present paper,the mathematic background of intrusive polynomial chaos (IPC) method and coupling process with one dimension Euler equation were introduced. The IPC method was implemented for the 2D compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a lid driven cavity flow under the influence of uncertainties. The driven velocity and fluid viscosity were supposed respectively to be the uncertain variable which has Gaussian probability distribution. Based on the validation with benchmark results,discussions were mainly focused on the statistic properties of velocity distribution. The results indicated the effect of IPC method on the simulation of propagation of uncertainty in the flow field. For the simulated results of 2D cavity flow,influence of the driven velocity uncertainty is larger than that of viscosity.
基金Project supported by the National Natural Science Foundation of China （Grant No 70271069）.
文摘By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.
基金the National Natural Science Foundation of China (Grants 41372301 and 51349011)the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109)
文摘A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.
文摘Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move at the same speed but in opposite directions so that symmetric flow patterns are generated. Similar to the Newtonian case, bifurcations occur as the aspect ratio decreases. Special to Bingham fluids, the non-Newtonian indicator, Bingham number B, also governs the bifurcation besides the bifurcation parameter A.
基金Project supported by the National Natural Science Foundation of China(No.50479053)
文摘Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.
