A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

Abstract

The present work is primarily concerned with studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. The flows of interest in the present case are assumed to be adequately represented by the compressible Reynolds-averaged Navier-Stokes equations, and the Spalart-Allmaras eddy viscosity model is used for turbulence closure. The equations are discretized in the context of a general purpose, density-based, unstructured grid finite volume method. Spatial discretization is based on the Steger-Warming flux vector splitting scheme and temporal discretization uses a backward Euler point-implicit integration. The work discusses in detail the theoretical and numerical formulations of the selected model. The computational studies consider the turbulent flow over a flat plate at 0.3 freestream Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. Moreover, the results also show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer. Finally, the paper also demonstrates how the spatial discretization scheme can be selectively modified to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications at the same time that it can accurately compute turbulent boundary layers.

A kinetic energy preserving nodal discontinuous Galerkin spectral element method

“…For discretizations with moderate polynomial degree, the dissipative nature of the DG method introduced through the approximate Riemann solver‐based flux functions becomes more prominent and may reduce the applicability of such methods for the direct or large eddy simulation of turbulent flows. It is especially the artificial over‐dissipation (or anti‐dissipation in some cases) of the kinetic energy that may have negative impact on the behavior of turbulent flows, see for example . A naive remedy for this problem would be to resort to central numerical flux approximations, but such a DG discretization suffers from severe robustness issues and instabilities, and it is furthermore not clear how the volume terms influence the consistency with respect to the kinetic energy balance.…”

Effects of Numerical Methods on the Calculation of Developing Plane Channel Flow

“…Therefore, the nature of the present investigation is different from those where the emphasis is concentrated on the more general effects of physical and numerical influences on turbulent flow calculations. Some relevant studies on the more general physical and numerical influences are represented by Launder and Spalding (1974) [8], Gunzburger and Labovsky (2012) [9], Junqueire-Juniot et al (2013) [10], Ahsan (2014) [11],…”

Study of Conservation on Implicit Techniques for Unstructured Finite Volume Navier-Stokes Solvers

“…Numerical studies performed in the present work indicated that this flux vector splitting is too dissipative and it can deteriorate the boundary layer profiles (JunqueiraJunior, 2012;Junqueira-Junior et al, 2013;MacCormack and Candler, 1989). Therefore, a pressure switch is implemented to smoothly shift the Steger-Warming scheme into a centered one.…”

“…Equation (27) applies the term to decrease the value at the faces parallel to the wall inside the boundary layer (Scalabrin, 2007). This artificial dissipation model has shown an important role in the prediction of boundary layer profiles (Junqueira-Junior, 2012;Junqueira-Junior et al, 2013).…”