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.