An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in ...An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.展开更多
The steady, asymmetric and two-dimensional flow of viscous, incompressible and Newtonian fluid through a rectangular channel with splitter plate parallel to walls is investigated numerically. Earlier, the position of ...The steady, asymmetric and two-dimensional flow of viscous, incompressible and Newtonian fluid through a rectangular channel with splitter plate parallel to walls is investigated numerically. Earlier, the position of the splitter plate was taken as a centreline of channel but here it is considered its different positions which cause the asymmetric behaviour of the flow field. The geometric parameter that controls the position of splitter is defined as splitter position parameter a. The plane Poiseuille flow is considered far from upstream and downstream of the splitter. This flow-problem is solved numerically by a numerical scheme comprising a fourth order method, followed by a special finite-method. This numerical scheme transforms the governing equations to system of finite-difference equations, which are solved by point S.O.R. iterative method. In addition, the results obtained are further refined and upgraded by Richardson Extrapolation method. The calculations are carried out for the ranges -1 α R < 10<sup>5</sup>. The results are compared with existing literature regarding the symmetric case (when a = 0) for velocity, vorticity and skin friction distributions. The comparison is very favourable. Moreover, the notable thing is that the decay of vorticity to its downstream value takes place over an increasingly longer scale of x as R increases for symmetric case but it is not so for asymmetric one.展开更多
基金supported by the National Natural Science Foundation of China(No.51174236)the National Basic Research Program of China(973 Program)(No.2011CB606306)the Opening Project of State Key Laboratory of Porous Metal Materials(No.PMM-SKL-4-2012)
文摘An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
文摘The steady, asymmetric and two-dimensional flow of viscous, incompressible and Newtonian fluid through a rectangular channel with splitter plate parallel to walls is investigated numerically. Earlier, the position of the splitter plate was taken as a centreline of channel but here it is considered its different positions which cause the asymmetric behaviour of the flow field. The geometric parameter that controls the position of splitter is defined as splitter position parameter a. The plane Poiseuille flow is considered far from upstream and downstream of the splitter. This flow-problem is solved numerically by a numerical scheme comprising a fourth order method, followed by a special finite-method. This numerical scheme transforms the governing equations to system of finite-difference equations, which are solved by point S.O.R. iterative method. In addition, the results obtained are further refined and upgraded by Richardson Extrapolation method. The calculations are carried out for the ranges -1 α R < 10<sup>5</sup>. The results are compared with existing literature regarding the symmetric case (when a = 0) for velocity, vorticity and skin friction distributions. The comparison is very favourable. Moreover, the notable thing is that the decay of vorticity to its downstream value takes place over an increasingly longer scale of x as R increases for symmetric case but it is not so for asymmetric one.
