A residual based eddy viscosity model for the large eddy simulation of turbulent flows

A new eddy viscosity model for the large eddy simulation of turbulent flows is developed. The eddy viscosity is proportional to the product of the magnitude of the fine scale velocity and the grid size. The residual based variational multiscale formulation is used to obtain a computationally inexpensive approximation for the fine scale velocity field. It is noted that the fine scale velocity field, and hence the eddy viscosity, are proportional to the residual of the resolved scale solution. As a result the eddy viscosity automatically vanishes whenever or wherever the coarse scale solution is accurate. In that regard this model is inherently dynamic and does not require the application of a dynamic procedure. The performance of this model is tested in predicting the decay of incompressible and compressible homogeneous turbulence. In both cases it is found that it is more accurate than the dynamic version of the Smagorinsky-type eddy viscosity model. In addition, it is easier to implement as it does not require a dynamic procedure in order to determine model parameters.