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