Improving the Numerical Accuracy of the k-ε Model by a Transformation to the k-τ Model

For geophysical and environmental high Reynolds number boundary layer flows we demonstrate that the numerical accuracy of the k-ε turbulence model can be improved by transforming the k-ε model into the k-τ model. This approach ensures that the k-τ model uses the same physical parameterisation as the k-ε model, hence the models differ only in numerical aspects.

A comparison between the two turbulence models is carried out using four idealised one-dimensional vertical (1DV) test cases. The test cases represent homogeneous and stratified flows typically encountered in rivers, estuaries and along the coast. The advantage of using a 1DV model is that it allows for convergence tests up to 2000 vertical layers. For homogeneous and stratified boundary layer flows the four cases show that the k-τ model is more accurate than the k-ε model. This holds for resolutions of 10 to more than 100 grid cells in the vertical direction. The improved accuracy comes without additional computational cost. With increasing vertical resolution the k-τ model convergences faster than the k-ε model. We explain the improved numerical performance of the k-τ model by the linearity of τ in the bed-boundary layer and the better-defined bed-boundary condition.