基于格子Boltzmann模型的Lee-Tarver爆轰波计算

The Computation of Lee-Tarver Detonation Based on Lattice Boltzmann Model

本文提出了高速可压格子Boltzmann模型与Lee-Tarver反应率函数相耦合的模型求解爆轰问题。格子Boltzmann模型使用两个平衡态分布函数分别描述反应物和产物的密度、动量和能量。在连续极限假设下,模型能够给出与Navier-Stokes方程一致的结果。由于化学反应过程和热动力学过程的时间尺度是分离的,所以采用算子分裂法求解Lee-Tarver反应率函数。为了验证模型的有效性,我们研究了爆轰波与冲击波的对撞问题以及爆轰波引发的Richtmyer-Meshkov不稳定性问题。数值结果表明,本文所提出的模型可以用来模拟爆轰现象。

In this paper, we present a high speed compressible lattice Boltzmann model coupled with Lee-Tarver reaction rate function for detonation. Two distribution functions are used to describe the density, momentum and energy of reactant and product in the lattice Boltzmann scheme, which gives consistent results with the Navier-Stokes equation in the continuum limit. Due to the separation of time scales in the chemical and thermodynamic process, the operator-splitting scheme is employed to solve Lee-Tarver reaction rate function. To indicate the validity of the model, we studied the collision between detonation and shock waves, the Richtmyer-Meshkov instability by detonation. The numerical examples show that the scheme can be used to compute the detonation phenomena.