An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems

Abstract : This paper deals a multiresolution strategy applied to a semi-intrusive scheme recently introduced by the authors in the context of uncertainty quantification (UQ) analysis for compressible fluids problems. The mathematical framework of the multiresolution framework is presented for the cell-average setting and the coupling with the existing semi-intrusive scheme is described from both the theoretical and practical point-of-view. Some reference test-cases are performed to demonstrate the convergence properties and the efficiency of the overall scheme: the linear advection problem for both smooth and discontinuous initial conditions, the inviscid Burgers equation and the 1D Euler system of equations to model an uncertain shock tube problem obtained by the well-known Sod shock problem. For all the cases presented, the convergence curves are computed with respect to semi-analytical solutions obtained for the stochastic formulation of the test cases. In the case of the shock tube problem, an original technique to obtain a reference high-accurate numerical stochastic solution has also been developed.
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[Research Report] RR-8688, INRIA Bordeaux, équipe CARDAMOM. 2015
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Rémi Abgrall, Pietro Marco Congedo, Gianluca Geraci, Gianluca Iaccarino. An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems. [Research Report] RR-8688, INRIA Bordeaux, équipe CARDAMOM. 2015. 〈hal-01120412v2〉

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