The Mathematical Theory Of Lattice Boltzmann Model For Compressible Flows

The lattice Boltzmann method is a new kind of computational fluid dynamics method. It has been widely used in fields of fluid dynamics and computational physics for years. The lattice Boltzmann method, as a new kind of computational fluid dynamics method, has been developed very quickly since 1992. It has been used in kinds of computational fluid dynamics fields. First, the lattice Boltzmann method is used to simulate the Navier-Stokes equations. Because it overcomes several defects of CA theory, the method is more convenient, more effective. After study of decades, it shows that the lattice Boltzmann method has utilized fields of itself. In these fields, it maybe can achieve the level of the traditional numerical method but can not in other fields. At present, the lattice Boltzmann method has developed from simply qualitative study to accurate quantitative compare. We may select the equilibrium distribution function according to the need of physical problem and can select precision. In the paper, our model possesses second-order precision. It has a suit of strict mathematical theory of itself and proofed physical bases. The conformation of compressible model is all along a studied problem to people. At present, people have some fruits at the simulation of Euler equations of perfect gas. But as second-order, the lattice Boltzmann model of simulating Navier-Stokes equations has no development all long. Nay, the conformation of the possessing energy lattice Boltzmann method is very difficult. Three-dimensional problems are unsuccessful all long. Shan. X.W's two kinds distribution theory accounts for it's coupling problem. Herein these problems, we extend bits to 25 and gained possessing energy compressible fluid dynamics equations. Truncation error is second-order. The paper uses different time scale series of equations accord to t Boltzmann equations　　　　　　 (1)　(2) 　　 (3)(4) (5)detrudes Navier-Stokes equations. The precision of the model is second-order. Using (5), we gained truncation error of the model(limited to length, we only write the truncation error of one of equations ). (6)Going through computing, we get coefficients of collide terms. Using Hirt heuristic stability theory, we get series of inequations. According to these inequations, we can confirm the scale of coefficients of equilibrium distribution functions. Then, we present the Boltzmann equations mathematical theory in compressible flows.