By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved...By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.展开更多
In the present paper,the classical pressure correction method was extended into low Mach number compressible flow regime by integrating equation of state into SIMPLE algorithm.The self-developed code based on this alg...In the present paper,the classical pressure correction method was extended into low Mach number compressible flow regime by integrating equation of state into SIMPLE algorithm.The self-developed code based on this algorithm was applied to predicting the lid-driven cavity flow and shock tube prob-lems,and the results showed good agreement with benchmark solutions and the Mach number can reach the magnitude of as low as 10-5.The attenuation of sound waves in viscous medium was then simulated.The results agree well with the analytical solutions given by theoretical acoustics.This demonstrated that the present method could also be implemented in acoustics field simulation,which is crucial for thermoacoustic simulation.展开更多
An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density...An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.展开更多
基金The project supported by the Basic Research on Frontier Problems in Fluid and Aerodynamics in Chinathe National Natural Science Foundation of China (19772069)
文摘By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.
基金Supported by the Key Project of National Natural Science Foundation of China(Grant Nos.50736005,50636050)
文摘In the present paper,the classical pressure correction method was extended into low Mach number compressible flow regime by integrating equation of state into SIMPLE algorithm.The self-developed code based on this algorithm was applied to predicting the lid-driven cavity flow and shock tube prob-lems,and the results showed good agreement with benchmark solutions and the Mach number can reach the magnitude of as low as 10-5.The attenuation of sound waves in viscous medium was then simulated.The results agree well with the analytical solutions given by theoretical acoustics.This demonstrated that the present method could also be implemented in acoustics field simulation,which is crucial for thermoacoustic simulation.
基金supported by the French"Commissariat´a l’Energie Atomique(CEA)"(Centre de Saclay)in the frame of the contract"ASTRE",#SAV 34160the Marie Curie Actions of the European Commission in the frame of the DEASE project(MESTCT-2005-021122)。
文摘An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.
