We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsu...We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 （2004） 035701（R）] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the yon Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include （i） Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, （ii） Regular and Mach shock reflections, and （iii） Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.展开更多
In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-...In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.展开更多
基金Supported by the Science Foundations of LCP and CAEP under Grant Nos.2009A0102005 and 2009B0101012the National Basic Research Program (973 Program) under Grant No.2007CB815105the National Natural Science Foundation under Grant Nos.10775018,10702010,and 10775088
文摘We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 （2004） 035701（R）] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the yon Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include （i） Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, （ii） Regular and Mach shock reflections, and （iii） Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.
基金supported by the National Basic Research Program of China(Grant No.2009CB724104)
文摘In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.
