An efficient unstructured WENO method for supersonic reactive flows

An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.