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Viscous dissipation in DG methods for turbulent incompressible flows
Author(s) -
Lehrenfeld Christoph,
Lube Gert,
Schroeder Philipp W.
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900049
Subject(s) - dissipation , turbulence , compressibility , discontinuity (linguistics) , mechanics , benchmark (surveying) , direct numerical simulation , physics , flow (mathematics) , mathematics , statistical physics , classical mechanics , mathematical analysis , reynolds number , geology , thermodynamics , geodesy
Nowadays, (high‐order) DG methods, or hybridised variants thereof, are widely used in the simulation of turbulent incompressible flow problems. For turbulence simulations, and especially in the practically relevant situation of strong under‐resolution, it is important to distinguish between the resolved physical dissipation rate and the contribution of numerical dissipation originating from the underlying method. In this note, a certain ambiguity related to such a decomposition for the viscous effects in a DG‐discretised fluid flow problem, which is due to the discontinuity of the approximate solution, is addressed. A novel but rather natural decomposition into ‘physical’ and ‘numerical’ viscous dissipation is proposed for a class of DG methods. Based on a typical 3D benchmark problem for decaying turbulence, its meaningfulness is confirmed numerically. In order to justify the term ‘dissipation’, both the physical and the numerical contributions for the proposed additive decomposition are provably non‐negative (possibly zero).