A symmetry-preserving second-order time-accurate PISO-based method. (15th July 2021)

• Record Type: Journal Article
• Authors: Komen, E.M.J.; Hopman, J.A.; Frederix, E.M.A.; Trias, F.X.; Verstappen, R.W.C.P.
• Is Part Of: Computers & fluids. Volume 225(2021)
• Publication Date: 2021-07-15
• Subjects: Symmetry-preserving discretisation -- Unstructured -- Collocated -- Runge-Kutta -- Conservative -- OpenFOAM; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2021.104979
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: A symmetry-preserving second-order time-accurate PISO-based method. Comparison with conservative symmetry-preserving projection method of Trias et al. (2014). Error sources causing the numerical dissipation. Both methods are effectively fully-conservative when an incremental-pressure approach is used. Abstract: A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method. Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods.