Abstract
In recent years the use of high-order Discontinuous Galerkin (DG) methods for the under-resolved direct numerical simulations (uDNS) of turbulent flows has received special attention. The suitability of the approach for this kind of applications is related to the dissipation and dispersion proprieties of the scheme: while the dispersion errors are small over a broad range of frequencies, a relevant dissipation error mainly acts at the smallest under-resolved scales, resembling a high frequency filter. Nevertheless, it was recognized (Flad and Gassner, 2017; Mengaldo et al., 2018) that the choice of the interface convective numerical flux strongly affects this dissipation behaviour and ultimately the success of the uDNS approach. In this regard, the excess of numerical dissipation caused by some upwind numerical convective fluxes must be avoided, in particular when dealing with low-speed flows, since this behaviour is exacerbated approaching the incompressibility limit. Fixes for the excess of numerical dissipation of these schemes have been proposed by several authors in the context of different numerical methods, see for example Weiss and Smith (1995). In this work a simple modification of the dissipation term of the low Mach preconditioned Roe scheme proposed by Weiss and Smith is considered. The aim is to reduce further the amount of numerical dissipation with the intent of improving the results of uDNS. A spatial DG discretization coupled with a linearly-implicit Rosenbrock-type time integrator is here considered as a numerical framework perfectly suited for the assessment and comparison of different numerical flux functions. Results on canonical turbulent flow problems as the Taylor–Green vortex and the flow in a straight sided channel are presented. The improved accuracy of the proposed flux function is demonstrated. The new low-dissipation flux can be useful also in the context of standard, lower order, finite volume methods.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.