Damping numerical oscillations in hybrid solvers through detection of Gibbs phenomenon

Abstract

Summary A Gibbs phenomenon detector that is useful in damping numerical oscillations in hybrid solvers for compressible turbulence is proposed and tested. It is designed to function in regions away from discontinuities where commonly used discontinuity sensors are ineffective. Using this Gibbs phenomenon detector in addition to a discontinuity sensor for combining central and shock capturing schemes provides an integrated way of dealing with numerical oscillations generated by shock waves and contact lines that are normal to the flow. When complete suppression of numerical oscillations is not possible, they are sufficiently localized. Canonical tests and large eddy simulations show that inclusion of the proposed detector does not cause additional damping of ‘well‐resolved’ physical oscillations. Copyright © 2017 John Wiley & Sons, Ltd.

r-adaptive algorithms for supersonic flows with high-order Flux Reconstruction methods

“…Originally developed by Huynh for 1D advection problems in [3], the FR method is a framework which allows to develop new high-order schemes while being simple and computationally efficient, particularly on graphical processor units (GPU) [4,5].Despite those advantages, the FR method suffers from the same pacing items as the other high-order methods such as the slow convergence to steady state and the lack of robust shock capturing methods [6]. When trying to approximate a discontinuity (such as a jump in a physical property due to a shock) with a polynomial representation, the Gibbs phenomenon causes a decrease in accuracy and leads to the appearance of spurious oscillations which can trigger instabilities in the numerical computations [7]. To solve this issue, different limiting and artificial viscosity (AV) strategies have been developed as summarized in [8].…”