Narrow Results

The nonlinear coupled constitutive relations (NCCR) has been studied intensively under structured finite-volume framework. For further engineering applications, it is necessary to study the potential capability of NCCR with the use of unstructured mesh. In this paper, a three-dimensional NCCR solver with hybrid unstructured techniques is developed on the basis of our in-house code. An upwind flux-splitting scheme with LU-SGS implicit time-marching scheme is employed. The accuracy of the developed NCCR solver is validated by two hypersonic cases, such as high-speed flows around 2D cylinder and 3D blunted cone tip in rarefied regimes. Computations show that the solver using hybrid unstructured techniques yields comparable good results as the structured one. Moreover, they can get solutions in better agreement with the Direct Simulation Monte Carlo (DSMC) than the NS results.

A new semilagrangian method is presented for the numerical solution of the BGK model of the Boltzmann equation in a domain with moving boundary. The method is based on discretization of the equation on a fixed grid in space and velocity. The equation is discretized in characteristic form, and the distribution function is reconstructed at the foot of the characteristics by a third order piecewise Hermite interpolation. Reflecting moving boundary at the piston are suitably described by assigning the value of the distribution function at ghost cells. A comparison with Euler equation of gas dynamics for the piston problem has been performed in the case of small Knudsen number.