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Upwind Finite-Volume Solution of Stochastic Burgers’ Equation
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
Department of Engineering Mathematics & Physics, Faculty of Engineering, Fayoum University, Fayoum, Egypt
- 1 Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
- 2 Department of Engineering Mathematics & Physics, Engineering Faculty, Cairo University, Giza, Egypt
- 3 Department of Engineering Mathematics & Physics, Faculty of Engineering, Fayoum University, Fayoum, Egypt
Applied Mathematics·Volume 03 (2012)·Pages 1818–1825·Published 27 November 2012·DOI10.4236/am.2012.331247
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Abstract
In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers’ equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers’ solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.
KeywordsPolynomial Chaos ExpansionStochastic Burgers’ EquationUpwind Finite-Volume Technique
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