High-Order CENO Finite-Volume Scheme with Anisotropic Adaptive Mesh Refinement: Efficient Inexact Newton Method for Steady Three-Dimensional Flows

A high-order finite-volume scheme with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method for the solution of steady compressible fluid flows governed by the Euler and Navier–Stokes equations on three-dimensional multi-block body-fitted hexahedral meshes. The proposed steady flow solution method combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with both a scalable and efficient Newton–Krylov–Schwarz (NKS) algorithm and a block-based anisotropic AMR method. 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 and makes use of a high-order representation of the mesh and a high-order treatment of boundary conditions. In the proposed Newton method, the resulting linear systems of equations 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 data structure and permits local anisotropic refinement of the grid in preferred directions as directed by appropriately specified physics-based refinement criteria. Numerical results are presented for a range of inviscid and viscous steady problems and the computational performance of the combined scheme is demonstrated and assessed.