A low-pass filter for linear forcing in the open-source code OpenFOAM – Implementation and numerical performance

Direct Numerical Simulations or Large-Eddy Simulations often require that turbulence is forced and maintained throughout the solution time in the complete computational domain. In numerical codes written in physical space—like the open source library OpenFOAM—a modeling technique called linear forcing is often used for this purpose. It consists of adding a body-force term to the Navier–Stokes equations which is linearly proportional to the velocity. When compared to codes written in spectral space, in physical space this technique can only capture integral length scales half the size of those in spectral codes and is therefore inferior in terms of numerical efficiency. As shown by Palmore and Desjardins 2018 ([1], Physical Review Fluids 3, 034605) this drawback can be overcome through low-pass filtering of the velocity field used for forcing. However, the filter proposed in [1], although one-dimensional, is implicit and increases considerably the CPU-time. In order to overcome this, the present work proposes a new three-dimensional, explicit, low-pass Laplace-filter which is numerically efficient, shows very good scaling features and is easy to implement and parallelize. With this, the integral length-scale of turbulence increases more than two times thus resolving successfully a larger scale range of turbulence. A second improvement proposed in this work concerns the particular form of the linear forcing term: it applies the forcing individually to each velocity component. It is found that the new forcing term prevents unphysical, numerically triggered growth of only one velocity component and hence stabilizes the numerical process in OpenFOAM.