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An adaptive multiresolution semi‐intrusive scheme for UQ in compressible fluid problems
Author(s) -
Abgrall R.,
Congedo P. M.,
Geraci G.,
Iaccarino G.
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4030
Subject(s) - inviscid flow , compressible flow , mathematics , compressibility , convergence (economics) , shock tube , shock (circulatory) , advection , burgers' equation , multiresolution analysis , mathematical optimization , mathematical analysis , computer science , partial differential equation , shock wave , wavelet , mechanics , physics , medicine , discrete wavelet transform , wavelet transform , artificial intelligence , economics , thermodynamics , economic growth
Summary This paper deals with the introduction of a multiresolution strategy into the semi‐intrusive scheme, recently introduced by the authors, aiming to propagate uncertainties in unsteady compressible fluid applications. The mathematical framework of the multiresolution setting is presented for the cell‐average case, and the coupling with the semi‐intrusive scheme is described from both the theoretical and algorithmic 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 an uncertain shock tube problem obtained by modifying the well‐known Sod shock problem. For all the cases, the convergence curves are computed with respect to semi‐analytical (exact) solutions. In the case of the shock tube problem, an original technique to obtain a reference highly‐accurate numerical stochastic solution has also been developed. Copyright © 2015 John Wiley & Sons, Ltd.