BOUNDARY PROCEDURES FOR THE TIME-DEPENDENT BURGERS' EQUATION UNDER UNCERTAINTY

作     者：Per Pettersson Jan Nordstrm Gianluca Iaccarino 

作者机构：Mechanical Engineering and Institute for Computational Mathematical EngineeringStanford University Division of Scientific ComputingDepartment of Information TechnologyUppsala University School of MechanicalIndustrial and Aeronautical EngineeringUniversity of the Witvatersrand Department of Aeronautics and Systems IntegrationFOIThe Swedish Defense Research Agency 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2010年第30卷第2期

页      面：539-550页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0714[理学-统计学（可授理学、经济学学位）] 0704[理学-天文学] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by the US Department of Energy under the PSAAP Program 

主　　题：stochastic Burgers' equation uncertainty quantification polynomial chaos 

摘      要：The Burgers＇ equation with uncertain initial and boundary conditions is approximated using a Polynomial Chaos Expansion （PCE） approach where the solution is represented as a series of stochastic, orthogonal polynomials. The resulting truncated PCE system is solved using a novel numerical discretization method based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. The resulting PCE solution yields an accurate quantitative description of the stochastic evolution of the system, provided that appropriate boundary conditions are available. The specification of the boundary data is shown to influence the solution; we will discuss the problematic implications of the lack of precisely characterized boundary data and possible ways of imposing stable and accurate boundary conditions.