An adaptive multiresolution semi‐intrusive scheme for UQ in compressible fluid problems. (27th March 2015) - Abgrall, R.; Congedo, P. M.; Geraci, G.; Iaccarino, G.
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.