A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations  

作　　者：Gaspar J.Machado Stéphane Clain Raphaël Loubère 

机构地区：[1]Centre of Physics and Department of Mathematics,University of Minho,Campus of Azurém,4800-058 Guimaraes,Portugal [2]CNRS and Institut de Mathématiques de Bordeaux(IMB),Universitéde Bordeaux,Talence,France

出　　处：《Communications on Applied Mathematics and Computation》2023年第2期751-775,共25页应用数学与计算数学学报（英文）

基　　金：support by FEDER-Fundo Europeu de Desenvolvimento Regional,through COMPETE 2020-Programa Operational Fatores de Competitividade,and the National Funds through FCT-Fundacao para a Ciencia e a Tecnologia,project no.UID/FIS/04650/2019;support by FEDER-Fundo Europeu de Desenvolvimento Regional,through COMPETI E 2020-Programa Operacional Fatores de Competitividade,and the National Funds through FCT-Fundacao para a Ciencia e a Tecnologia,project no.POCI-01-0145-FEDER-028118

摘　　要：We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

关 键 词：Finite volume MOOD Adaptive stencil Steady-state solution Euler equations High order 

分 类 号：O17[理学—数学]