DEVELOPMENT OF NON-OSCILLATORY LATTICE BOLTZMANN METHOD FOR FLOWS WITH SHOCK WAVES

The Lattice Boltzmann Method is a promising numerical scheme for the simulation of complex fluid flow problems. Most of the current LBM applications are restricted, however, to incompressible or weakly compressible flows. Increasing interest in LBM for simulating compressible flows in the last years caused a proliferation of methods proposed for the extension of LBM to compressible flows. In addition to the problems of aero-thermodynamics nature due to compressibility, another effect of high Mach number flows is the occurrence of shock waves which has to be accounted for in the numerical simulations. In the present work, a new approach that automatically switches from a high-order accurate scheme in smooth flow regions to a low-order diffusive scheme across shock wave, mimicking the use of upwind schemes and limiters in the classical CFD, is proposed. This scheme, implemented in the basis of the open-source package PyLBM, is described in the framework of Multi Relaxation Times (MRT) and extended to a family of vectorial schemes. The accuracy of the scheme is demonstrated for flows with discontinuities solved using the one-dimensional Burgers equation and one-, and two-dimensional Euler equation systems. The model is easily adaptable to different types of schemes and shows interesting features when applied to test cases with shock waves.