Predicting shock dynamics in the presence of uncertainties

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 bot...

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Bibliographic Details
Published in:Journal of computational physics 2006-09, Vol.217 (1), p.260-276
Main Authors: Lin, G., Su, C.-H., Karniadakis, G.E.
Format: Article
Language:English
Subjects:
AERODYNAMICS
ANALYTICAL SOLUTION
Apexes
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computer simulation
EQUATIONS
IDEAL FLOW
Polynomial chaos
POLYNOMIALS
Random inflow
RANDOMNESS
SHOCK WAVES
SIMULATION
STOCHASTIC PROCESSES
Stochastic simulations
Stochasticity
Supersonic aircraft
SUPERSONIC FLOW
TIME DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS
Wedges
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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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2006.02.009