  In this paper we presented a lattice Boltzmann with square grid for
compressible flow problems. Triple level velocity is considered for each cell.
Migration step use discrete velocity but continuous parameters are utilized to
calculate density, velocity, and energy. So, we called this semi-discrete
method. To evaluate the performance of the method the well-known shock tube
problem is solved, using 1-D and 2-D version of the lattice Boltzmann method.
The results of these versions are compared with each other and with the results
of the analytical solution.
