Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems

We construct stable, maximal order boundary closures for high order central difference methods. The stability is achieved by adding a small number of additional subcell nodes near the boundaries at experimentally determined locations. We find that methods up through 8th order can be stabilized by the addition of a single node, up through 16th order by the addition of two nodes, and up through 22nd order with three extra nodes. We also consider the application of the technique to dispersion relation preserving methods, and we construct and test artificial dissipation operators.