Learn More
Keywords: Uncertainty quantification Separated representation Alternating least-squares Curse of dimensionality Stochastic partial differential equations a b s t r a c t Uncertainty quantification schemes based on stochastic Galerkin projections, with global or local basis functions, and also stochastic collocation methods in their conventional form, suffer(More)
This paper demonstrates the use of polynomial chaos expansions (PCEs) for the non-linear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor-products of univariate orthogonal polynomial bases, PCEs approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include(More)
We propose a method for the approximation of solutions of PDEs with stochas-tic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a(More)
Keywords: Uncertainty quantification Padé–Legendre approximation Gibbs phenomenon Shock capturing Dual throat nozzle RAE2822 a b s t r a c t A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require(More)
SUMMARY We present a numerical method to study convective heat transfer in a high Reynolds number incompressible flow around a cylinder subject to uncertain boundary conditions. We exploit the one-way coupling of the energy and momentum transport to derive a semi-intrusive uncertainty propagation scheme, which combines Galerkin and collocation approaches(More)
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect of the unresolved fine scales through a model term that contains a fine-scale stochastic Green's function. For a(More)
On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random Abstract The stochastic Galerkin and collocation methods are used to solve an advection-diffusion equation with uncertain and spatially varying viscosity. We investigate well-posedness, monotonicity and stability for the extended system(More)