[Xiaoyu Yang]

Dear All,

First of all, wish you all have a successful year in 2017! I am relatively new to this forum and to OpenFOAM and LES. Thanks for your suggestions in advance!

At the moment, I am trying to validate the code and the LES model via a fully developed incompressible turbulent channel case at Re_tau=180. The pisoFoam solver together with the dynamicKEqn LES model are used. Please I was wondering if anyone could give me some suggestions on how to choose a proper combination of numerical schemes. Instead of the default, I am seeking for higher order schemes for lower dissipation and better accuracy.

The geometry of this rectangular channel is (2\pi\delta, 2\delta, \pi\delta) in the (x, y, z) directions, respectively. For Re_tau=180, the Reynolds number based on the mean centreline velocity is Re_delta=3300, and the kinematic viscosity is scaled such that the half channel height is 1m and the mean centreline velocity is 1m/s. Accordingly, to drive the flow, a corresponding constant x-momentum source term is implemented as a dynamic code through fvOptions. In accordance with this case setup, the periodic boundary conditions (cyclic B.C.) are applied in both the streamwise and spanwise directions.

Comparison results of the mean velocity and the Reynolds stress with DNS (Moser, Kim, and Moin 1999) are attached. As can be seen, the numerical accuracy needs to be improved, and I am struggling with choosing a proper combination of numerical schemes for higher order accuracy. At the moment, the Crank Nicolson scheme with the coefficient 0.9 is used for time integration, and the Gauss cubic scheme is used for the gradient terms. Linear interpolation and Gauss linear corrected Laplacian terms are also used. The used fvSchemes, the fvSolution, and the turbulenceProperties files are also attached for clarity.

Particularly, if the Gauss cubic scheme is used for the divergence terms, the instantaneous flow structures show irregular discontinuities even though the solver could still run.

Besides, at this stage, my primary consideration is about the numerical schemes. To get more familiar with this flow solver, and to save time and get some quick answers, a coarse mesh is used for the current computation. The used grid density is about the half of the standard LES requirements in all the three directions, i.e. dx+=28, dz+=19, dy+_1st=0.36, and dy+_max=37. The noslip wall boundary condition is applied for the top and the bottom walls with the viscous sublayer resolved.

Currently, I am using OpenFOAM-v3.0+ version. It seems that the Crank Nicolson scheme is a good choice for time integration. However, when with the coefficient 1.0, this implementation of the code becomes unstable and the flow diverges. Therefore, I am using the coefficient 0.9. For spatial discretizations, generally, I am trying to find a fourth order combination, preferably with lower dissipation.

Please could anyone give me some suggestions for this.

Thanks for your time!

Xiaoyu