A Robust Adaptive Solution Strategy for High-Order Implicit CFD Solvers

Abstract

This paper presents a solution approach for steady state forms of nonlinear systems of partial differential equations with physical realizability constraints. The main advantage of the approach is the insertion of feasibility constraints in the iterative solution path such that intermediate states before convergence are physically realizable. The method is specially suited for coarse meshes where regular pseudo-transient methods may lead to non-physical states. We present a technique for including the constraints in the solution path that seeks to improve the robustness, with respect to physical realizability, of the iteration to zero residual. In addition, we introduce an adaptive indicator that attempts to localize the cells that are preventing convergence when the solver fails to obtain a zero-residual solution. Results are presented in the context of adaptive mesh refinement for laminar and Reynolds-Averaged Navier-Stokes (RANS) flows with highly-under-resolved starting meshes.