基于二维紧凑型四阶格子模型的激波管流动模拟

为了提高格子的稳定性，使用Hermite展开方法，构建了新的二维四阶紧凑型格子模型，即D2Q37A。比较了D2Q37A和与Philippi给出的紧凑型格子模型(D2Q37B)的稳定性。在相同的碰撞频率下，与D2Q37B相比，D2Q37A可以模拟初始密度比更高的一维激波管流动。这表明D2Q37A与现有格子模型相比，具有更好的稳定性。详细给出了适用于高阶格子模型的边界条件实现方式。此边界条件实现方式保留了体现LBM（lattice Boltmann method）粒子特性的迁移 碰撞机制。用以上给出的格子模型和边界条件处理方式模拟激波管流动，得到的模拟结果和解析解吻合得很好。这表明所给出的边界处理方式是可行的。此边界格式同样可以用于其他类型的流动和边界。 

Simulating shock tube flow with a two dimensional compact fourth order lattice model

In order to improve the stability of the lattice model, a new two dimensional compact fourth order lattice model, ie, D2Q37A,was constructed based on the Hermite expansion. The stability of D2Q37A and the one proposed by Philippi (D2Q37B) were compared. Under the same collision frequency, D2Q37A can be applied to the one dimensional shock flow with the higher initial density ratio comparing with D2Q37B.That means D2Q37A was more stable than D2Q37B.An implementation of boundary conditions for high order lattice models was proposed in details. The implementation maintained the streaming collision mechanism ensuring the particle feature of the LBM（lattice Boltmann method）. This new lattice model and implementation of boundary conditions were applied to one dimensional shock tube problem and the result of simulation was consistent with the analytical solution. The results show the proposed boundary condition scheme is practicable. The proposed boundary scheme can be employed by other type of flow and boundary.