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

doi:10.1016/S0252-9602(10)60061-6

Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (2): 539-550.doi: 10.1016/S0252-9602(10)60061-6

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

Per Pettersson, Jan Nordstrom, Gianluca Iaccarino

1.Mechanical Engineering and |Institute for Computational Mathematical Engineering, Stanford University, Stanford, CA94305, USA；

2.Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-75105 Uppsala, Sweden；

3.School of Mechanical, Industrial and Aeronautical Engineering, University of the Witvatersrand, PO WITS 2050, Johannesburg, South Africa； 4.Department of Aeronautics and Systems Integration, FOI, The Swedish Defense Research Agency, SE-164 90 Stockholm, Sweden

Received:2009-12-16 Online:2010-03-20 Published:2010-03-20
Supported by:
Supported by the US Department of Energy under the PSAAP Program.

Abstract

Abstract:

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.

Key words: stochastic Burgers’equation, uncertainty quantification, polynomial chaos

CLC Number:

35R60

Per Pettersson, Jan Nordstrom, Gianluca Iaccarino. BOUNDARY PROCEDURES FOR THE TIME - DEPENDENT BURGERS’EQUATION UNDER UNCERTAINTY[J].Acta mathematica scientia,Series B, 2010, 30(2): 539-550.

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

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