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Predicting shock dynamics in the presence of uncertainties. (English) Zbl 1146.76613
Summary: We revisit the classical aerodynamics problem of supersonic flow past a wedge but subject to random inflow fluctuations or random wedge oscillations around its apex. We first obtain analytical solutions for the inviscid flow, and subsequently we perform stochastic simulations treating randomness both as a steady as well as a time-dependent process. We use a multi-element generalized polynomial chaos (ME-gPC) method to solve the two-dimensional stochastic Euler equations. A Galerkin projection is employed in the random space while WENO discretization is used in physical space. A key issue is the characteristic flux decomposition in the stochastic framework for which we propose different approaches. The results we present show that the variance of the location of perturbed shock grows quadratically with the distance from the wedge apex for steady randomness. However, for a time-dependent random process the dependence is quadratic only close to the apex and linear for larger distances. The multi-element version of polynomial chaos seems to be more effective and more efficient in stochastic simulations of supersonic flows compared to the global polynomial chaos method.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
65P20 Numerical chaos
76J20 Supersonic flows
76M10 Finite element methods applied to problems in fluid mechanics
76M35 Stochastic analysis applied to problems in fluid mechanics
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