Increasing the convergence rate to steady-state by using multiple penalty terms applied in a domain

Abstract

We introduce a new weak boundary procedure for high order finite difference methods applied to the linearized Euler and Navier-Stokes equations using summation-by-parts operators. Stability is obtained by using weak boundary conditions on penalty form. We demonstrate how to add on multiple penalties in the near boundary domain such that stability is preserved and an increased speed of convergence to steady-state is obtained.