Application of the Entropically Damped Artificial Compressibility model to direct numerical simulation of turbulent channel flow

The feasibility of the Entropically Damped Artificial Compressibility (EDAC) model for simulation of wall-bounded turbulence is examined. A favourable feature of EDAC is the purely parabolic type of governing equations resulting from the introduction of a damping term to the pressure evolution equation. This significantly reduces noise in the velocity divergence field when central schemes are applied for the spatial discretisation. The method of lines is used for the solution of the EDAC equations. A conservative finite difference method of purely 2nd- and mixed 4th/2nd-order is applied. The explicit 4th-order, six-stage low storage Runge Kutta method is used for time advancement. As expected, the mixed scheme is superior to the 2nd-order one in terms of both accuracy and computational efficiency. For the first time, the EDAC model is assessed for the direct numerical simulation of wall-bounded turbulent flow requiring a non-uniform mesh. As a particular test case we have chosen the channel flow at the friction Reynolds numbers Re-tau = 180 and 395. A very good agreement with the reference data is obtained, as documented by the chosen one-point velocity statistics: the mean and r.m.s. profiles and the budgets of the Reynolds stresses. The use of the explicit time discretisation and local (rather than compact) spatial schemes results in easily and efficiently parallelisable solution algorithm. We achieved very high computational performance on a desktop computer when solving the EDAC equations using a code dedicated for the graphics processing unit (GPU). The aspects of the GPU implementation are discussed. (C) 2018 Elsevier Ltd. All rights reserved.