A constrained boundary gradient reconstruction method for unstructured finite volume discretization of the Euler equations

Abstract

We propose a novel boundary gradient and solution reconstruction approach for the second-order cell-centered unstructured finite volume method for solving the inviscid Euler equations. The proposed constrained reconstruction method involving ghost cells is shown to be more accurate than several conventional boundary reconstruction methods and linear-exact in the near-boundary areas. In the present procedure, the solutions at the ghost cell centroids are given by solving constraint equations, which are established based on boundary conditions. At the same time, the solution gradients in boundary cells and the solutions in boundary surfaces are obtained altogether, while guaranteeing the compatibility of the boundary conditions with the reconstructed results. A variety of numerical test cases show that the new method effectively reduces the errors of near-boundary approximations and improves the overall numerical accuracy. Furthermore, because the constrained reconstruction is only used for the boundary cells, the extra computational cost barely changes the overall computational efficiency.