High-order finite elements applied to the discrete Boltzmann equation

A discontinuous Galerkin approach for solving the discrete Boltzmann equation is presented, allowing to compute approximate solutions for fluid flow problems. Based on a two-dimensional high-order finite element and an explicit Euler time stepping scheme, the D2Q9 model is discretized and the results are compared to the exact solution of the Navier–Stokes equation. Four numerical examples are considered, including stationary and instationary problems with curved boundaries. It is demonstrated that the proposed method allows to obtain the desired, highly efficient exponential convergence