Boundary optimized diagonal-norm SBP operators

By using non-equispaced grid points near boundaries, we derive boundary optimized first derivative finite difference operators, of orders up to twelve. The boundary closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids. The new operators lead to significantly more efficient numerical approximations, compared with traditional SBP operators on equidistant grids. We also show that the non-uniform grids make it possible to derive operators with fewer one-sided boundary stencils than their traditional counterparts. Numerical experiments with the 2D compressible Euler equations on a curvilinear multi-block grid demonstrate the accuracy and stability properties of the new operators.