Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were de...Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.展开更多
In this paper,a divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the non-staggered grid is presented.The exact discrete projection method is use...In this paper,a divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the non-staggered grid is presented.The exact discrete projection method is used to compute the velocity field,which ensures the discrete divergence of the velocity field is zero.In order to eliminate the odd-even decoupling in the pressure field,a filtering procedure is proposed and applied to the pressure field.We have shown this filter recovers the grid scale ellipticity in the pressure field and the odd-even decoupling can be removed effectively.The proposed numerical scheme is further verified through numerical experiments.展开更多
2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curviline...2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curvilinear coordinate system and the elliptic differential equations are used to generate curvilinear grids, so a model in generalized curviline ar coordinate is presented to simulate 2D horizontal cooling water, Governing equations of the model are discretized by finite volume method, and non-staggered grids and SIMPLE algorithm are introduced to simplify the program during the discretization. This model is used to simulate the movement of cooling water in a simplified meandering channel and a natural channel, calculating results indicate this model can correctly reflect the movement rules of cooling water, which verifies the model can be applied in engineering practice.展开更多
The laminar and turbulent flows past an axi-symmetric body with a ring wingwere investigated numerically at various attack angles (0°-20°) for the Reynolds numbers rangingfrom 10~3 to 10~7. The DDM (Domain D...The laminar and turbulent flows past an axi-symmetric body with a ring wingwere investigated numerically at various attack angles (0°-20°) for the Reynolds numbers rangingfrom 10~3 to 10~7. The DDM (Domain Decomposition Method) with the Schwarz iterative method based onfinite difference approximation was applied to simulate this problem. The primitive variableformulation was used for the solution of the incompressible Navier-Stoke equations. The velocityfield was calculated from the unsteady momentum equation by marching in time. The continuityequation was replaced by a Poisson-type equation for the pressure with the Neumann boundaryconditions. The Baldwin-Lomax model was adopted to simulate turbulence effect. The leap frogimplicit iterative method was used for the time difference approximations. The computed pressure atthe front stagnation point is found to have a small deviation, less than 10%, from the theoreticalvalue. The outlet flux has a loss about 5%. The lift coefficients increase linearly with the attackangle, but for attack angles greater than 15° the lift coefficients show mild decrease. Thefriction drag coefficients are insensitive to the attack angles, but the pressure drag coefficientsincrease markedly with the attack angles. In addition, complex flow patterns are revealed within thevicinity of the ring wing.展开更多
In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theo...In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields.The inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.The remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions.To achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations.Through the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.展开更多
This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized cu...This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.展开更多
文摘Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.
文摘In this paper,a divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the non-staggered grid is presented.The exact discrete projection method is used to compute the velocity field,which ensures the discrete divergence of the velocity field is zero.In order to eliminate the odd-even decoupling in the pressure field,a filtering procedure is proposed and applied to the pressure field.We have shown this filter recovers the grid scale ellipticity in the pressure field and the odd-even decoupling can be removed effectively.The proposed numerical scheme is further verified through numerical experiments.
基金Project supported by the National 973 Program(Grant No :2003CB415203) ,and the National Natural Science Founda-tion of China (Grant No :50579054)
文摘2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curvilinear coordinate system and the elliptic differential equations are used to generate curvilinear grids, so a model in generalized curviline ar coordinate is presented to simulate 2D horizontal cooling water, Governing equations of the model are discretized by finite volume method, and non-staggered grids and SIMPLE algorithm are introduced to simplify the program during the discretization. This model is used to simulate the movement of cooling water in a simplified meandering channel and a natural channel, calculating results indicate this model can correctly reflect the movement rules of cooling water, which verifies the model can be applied in engineering practice.
文摘The laminar and turbulent flows past an axi-symmetric body with a ring wingwere investigated numerically at various attack angles (0°-20°) for the Reynolds numbers rangingfrom 10~3 to 10~7. The DDM (Domain Decomposition Method) with the Schwarz iterative method based onfinite difference approximation was applied to simulate this problem. The primitive variableformulation was used for the solution of the incompressible Navier-Stoke equations. The velocityfield was calculated from the unsteady momentum equation by marching in time. The continuityequation was replaced by a Poisson-type equation for the pressure with the Neumann boundaryconditions. The Baldwin-Lomax model was adopted to simulate turbulence effect. The leap frogimplicit iterative method was used for the time difference approximations. The computed pressure atthe front stagnation point is found to have a small deviation, less than 10%, from the theoreticalvalue. The outlet flux has a loss about 5%. The lift coefficients increase linearly with the attackangle, but for attack angles greater than 15° the lift coefficients show mild decrease. Thefriction drag coefficients are insensitive to the attack angles, but the pressure drag coefficientsincrease markedly with the attack angles. In addition, complex flow patterns are revealed within thevicinity of the ring wing.
基金supported by the National Science Council of the Republic of China under the Grants NSC96-2221-E-002-293-MY2,NSC96-2221-E-002-004,and CQSE97R0066-69.
文摘In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields.The inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.The remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions.To achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations.Through the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.
基金The project was supported by the Natural Science Foundation of Zhejiang Province(196045)the National Natutal Science Foundation of China(19472055).
文摘This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.
