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978-3-8439-1261-7, Reihe Mathematik
Stochastic models for nonlinear convection-dominated flows
125 Seiten, Dissertation Universität Stuttgart (2013), Softcover, A5
This thesis consists of two parts. In the first part we introduce the hybrid stochastic Galerkin (HSG) method of the uncertainty quantification that extends the classical polynomial chaos approach by multi-resolution discretization of the stochastic space. Further we apply the HSG method on two real world examples. The first example deals with the nonlinear conservation law, describing continuous sedimentation processes in a clarifier-thickener with a random feed. The second example describes two-phase flows in a heterogeneous porous medium. The spatial position of the heterogeneity is randomly perturbed. The uncertainty quantification is performed by a HSG method. We show that the HSG method allows efficient parallelisation and present a stochastic adaptivity method. Numerical experiments cover one- and two-dimensional situations.
The second part inverstigates finite volume schemes for the scalar stochastic balance law with multiplicative noise. We establish the pathwise convergence of a semi-discrete finite volume solution towards a stochastic entropy solution. Numerical results illustrate the analytical findings.