An explicit algorithm for imbedding solid boundaries in Cartesian grids for the reactive Euler equations

We present a local and point-wise scheme for imposing reflective boundary conditions to stationary internal boundaries for solving the reactive Euler equations on Cartesian grids. The scheme is presented in two and three dimensions and can run efficiently on parallel machines while still maintaining the same advantages over other methods for enforcing internal boundary conditions. Level sets are used to represent internal solid regions along with a new local node sorting algorithm that decouples internal boundary nodes by establishing their connectivity to other internal boundary nodes. This approach allows us to enforce boundary conditions via a direct procedure, removing the need to solve a coupled system of equations numerically. We examine the accuracy and fidelity of our internal boundary algorithm by simulating flows past various solid boundaries in two and three dimensions, showing good agreement between our numerical results and experimental data.