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All fluid dynamic equations have their intrinsic modeling scales, such as the mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes equations. The current computational fluid dynamics (CFD) is a direct discretization of these partial differential equations (PDEs). Even with limited mesh size, the CFD targets to recover the exact solution of the PDEs as mesh size and time step approaching to zero. Under such a CFD methodology, the best result is to luckily get the exact solution of the governing equation. But, the flow physics is still limited by the modeling scale of the original governing equation. In reality, due to the limited cell resolution, we can never get the exact solution of these equations, and the limited mesh size and time step seem to introduce numerical errors only.
In a discretized space with limited cell resolution, the aim of CFD should directly model and simulate the flow motion in the mesh size and time step scales. With the variation of the ratio between the mesh size and the local particle mean free path, a direct modeling should be able to capture the flow physics from the kinetic scale particle collision and transport to the hydrodynamic scale wave propagation. The unified gas kinetic scheme is constructed under such a direct modeling principle. A continuum spectrum of governing equations from the kinetic to the hydrodynamic scales can be recovered in the direct modeling CFD method.
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ÐìÀ¥, Ïã¸Û¿Æ¼¼´óѧÊýѧϵ½ÌÊÚ, ÓÚ1987Äê±±¾©´óѧÌìÌåÎïÀíϵ±ÏÒµ, »ñµÃCUSPEA½±Ñ§½ð, ¸°ÃÀ¹ú¸çÂ×±ÈÑÇ´óѧ¹¥¶Á²©Ê¿Ñ§Î», 1993Äêµ½1996ÄêÔÚÆÕÁÖ˹¶Ù´óѧ, ʦ´Ó A. Jameson ½ÌÊÚ½øÐв©Ê¿ºó×êÑС£1996Äêµ½Ïã¸Û¿Æ¼¼´óѧÊýѧϵ¹¤×÷, ÖØÒª´ÓÊ»ùÓÚÆøÌ嶯ÀíÂÛµÄÍÆËãÁ÷ÌåÁ¦Ñ§²½Öè×êÑÐ,ÐìÀ¥½ÌÊÚÊǹú¼ÊÍÆËãÁ÷ÌåÁ¦Ñ§ÁìÓò³ÛÃûѧÕߣ¬Ä¿Ç°µ£ÈÎInternational Journal of Computational Fluid Dynamics, Communications in Computational Physics ºÍComputers and FluidsÔÓÖ¾¸±Ö÷±à¡£
