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Cited by 173 publications
(177 citation statements)
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“…When the number N q of collocation points is not sufficient and the response of the system is very sensitive to the uncertainty, it may happen that the typical distance between two neighboring shocks Dx sq is much larger than Dx. In this case, Dx sq ) Dx and the problem described hereinbefore appears, Poëtte et al [19]. However, several of our studies (not all presented here) have shown that the profiles recover regularity when we increase N q as Dx sq !…”
Section: Numerical Convergencesupporting
confidence: 55%
See 1 more Smart Citation
“…When the number N q of collocation points is not sufficient and the response of the system is very sensitive to the uncertainty, it may happen that the typical distance between two neighboring shocks Dx sq is much larger than Dx. In this case, Dx sq ) Dx and the problem described hereinbefore appears, Poëtte et al [19]. However, several of our studies (not all presented here) have shown that the profiles recover regularity when we increase N q as Dx sq !…”
Section: Numerical Convergencesupporting
confidence: 55%
“…For stochastic collocation techniques, we can mention among others the work of Foo et al [4], Witteveen and Bijl [27]. Poëtte et al [19] propose a stochastic intrusive approach to tackle shocks in compressible gas dynamics. Their gPC-based technique relies on the decomposition of the entropic variable of the flow and does not depend on a special discretization of the random space.…”
Section: Introductionmentioning
confidence: 99%
“…Consider (21) and assume that (A, B, C, D) ∈ U n with n ≥ 2 is given. We will construct (α, β, γ, δ) ∈ U 1 and (a, b, c, d) ∈ U n−1 which all satisfy (21). It will prove the theorem by descending iteration on n. The proof proceeds in several elementary steps.…”
Section: Proof Obviousmentioning
confidence: 99%
“…A third example is from reduced modeling, typically with POD techniques [17], and from interpolation on a sparse grid [14]. Uncertainty quantification intrusive techniques are also highly demanding in terms of having polynomial approximations with a priori unconditional respect of the maximum principle [21,7].…”
Section: Introductionmentioning
confidence: 99%
“…al. [17] used a nonlinear projection method to bound the oscillations close to stochastic discontinuities by gPC expansion of the entropy variables obtained from a transformation of the conservative variables. Each time step is complemented by a functional minimization to obtain the entropy variables needed to update the solution vector.…”
Section: Introductionmentioning
confidence: 99%