High-order finite-volume scheme with anisotropic adaptive mesh refinement: Efficient inexact newton method for steady three-dimensional flows

A high-order finite-volume method with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method integration scheme and described for the solution of compressible fluid flows governed by Euler and Navier-Stokes equations on three-dimensional multi-block body-fitted hexahedral meshes. The proposed approach combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a scalable and efficient Newton-Krylov-Schwarz (NKS) algorithm and a block-based anisotropic AMR. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions (even for smooth extrema) and non-oscillatory transitions at discontinuities. The implicit time stepping scheme is based on Newton’s method where the set of linear systems are solved using the generalized minimal residual (GMRES) algorithm preconditioned by a domain-based additive Schwarz technique. The latter uses the domain decomposition provided by the block-based AMR scheme leading to a fully parallel implicit approach with an efficient scalability of the overall scheme. The anisotropic AMR method is based on a binary tree and hierarchical data structure to permit local anisotropic refinement of the grid in preferred directions as directed by appropriately specified physics-based refinement criteria. Application and numerical results will be discussed for several steady inviscid and viscous problems and the computational performance of the overall scheme is demonstrated for a range of fluid flows.