A Higher-order multidimensional upwind solution-adaptive multigrid solver for compressible flows

A solution-adaptive local refinement multigrid strategy previously developed for a simple-wave model of the Euler equations has been extended to two newly developed higher-order-accurate characteristic decomposition methods for the solution of steady inviscid compressible flows. Numerical results show that the new methodology provides a significant accuracy improvement with respect to the simple-wave approach, at the expense of a reduced multigrid convergence rate. With its second-order spatial accuracy and very low entropy generation, the new method appears to be well suited for computing viscous flows.