Unsteady compressible flow computations using an adaptive multiresolution technique coupled with a high-order one-step shock-capturing 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 compress- ible flows in the transsonic 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 preserv- ing (MP) criterion is added in order to locally relax the TVD contraints 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 dynami- cally 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 7th order OSMP schemes coupled with adap- tive 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.
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