Unsteady compressible flow computations using an adaptive multiresolution technique coupled with a high-order one-step shock-capturing scheme. (5th October 2015) - Tenaud, Christian; Roussel, Olivier; Bentaleb, Linda
Highlights: We evaluate the capability of the adaptive multiresolution technique. We review the influence of the accuracy of the approximation scheme. We show the influence of the perturbation error related to ϵ parameter. We propose a specific ϵ value that saves CPU-time and memory usage. This specific ϵ value does not spoil the excellent accuracy of OSMP7 scheme. Abstract: This article deals with the development of adaptive multiresolution coupled with a one-step shock-capturing scheme for the numerical simulation of unsteady compressible flows in the transonic and supersonic regimes with high frequency oscillations. The discretization of the convective terms is based on a coupled time and space approach by using a one-step (OS) scheme, developed following the Lax–Wendroff approach by correcting the successive modified equations. A monotonicity preserving (MP) criterion is added in order to locally relax the TVD constraints for such schemes. The adaptive strategy relies on the Harten cell-average multiresolution analysis, with a dynamical data structure organized as a graded tree that dynamically evolves in time. We apply the method to several prototype test-cases of shock-wave propagation interaction. We validate this approach on 2D inviscid advection of a vortex. We then present 2D viscous test-cases of shock-shear layer interactions and a 3D spherical Riemann problem to demonstrate the capability of the present method. Results demonstrate that 7 th order OSMP schemes coupled with adaptive grid refinement gives very accurate results in comparison with more classical schemes applied on a single grid. We then propose an appropriate MR threshold parameter value that ensures accurate results while achieving drastic gains on the CPU time and memory usage.