Numerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemes

作     者：Stefan Berres Raimund Burger Alice Kozakevicius 

作者机构：Departamento de Ciencias Matematicas y FısicasUniversidad Catolica de TemucoTemucoChile CI2MA and Departamento de Ingenier´ıa Matem´aticaFacultad de Ciencias Fısicas y Matem´aticasUniversidad de Concepci´onCasilla 160-CConcepci´onChile Departamento de Matematica-CCNEUniversidade Federal de Santa MariaAv.Roraima1000Campus Universit´arioSanta MariaRSCEP 97105-900Brazil 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2009年第1卷第5期

页      面：581-614页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：support by Conicyt(Chile)through Fondecyt project 11080253 RB acknowledges support by Conicyt(Chile)through Fondecyt project 1090456,Fondap in Applied Mathematics,project 15000001 BASAL project CMM,Universidad de Chile and Centro de Investigacion en Ingenierıa Matematica(CI2MA),Universidad de Concepcion.AK is supported by CNPq project No.476022/2007-0 

主　　题：Hyperbolic-elliptic system conservation law oscillation wave numerical simulation multiresolution method sedimentation model 

摘      要：The generic structure of solutions of initial value problems of hyperbolic-elliptic systems,also called mixed systems,of conservation laws is not yet fully *** reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity *** is,however,theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations,so-called oscillatory waves,which are(in general,measure-valued)solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic *** capture these solutions,usually a fine computational grid is *** this work,a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave *** hyperbolic-elliptic 2×2 systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse *** the latter case,varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space,giving rise to different kinds of oscillation waves.