Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-order Runge–kutta Schemes

Nowadays open-source CFD codes provide suitable environments for implementation and testing low-dissipative algorithms typically used for turbulence simulation. Moreover these codes produce a reliable tool to test high-fidelity numerics on unstructured grids, which are particularly appealing for industrial applications. Therefore in this work we have developed several solvers for incompressible Navier–Stokes equations (NSE) based on high-order explicit and implicit Runge–Kutta (RK) schemes for time-integration. Note that for NSE space discretization the numerical technology available within OpenFOAM (Open-source Field Operation And Manipulation) library was used. Specifically in this work we have considered explicit RK projected type schemes for index 2 DAE system and L-stable Singly Diagonally Implicit Runge–Kutta (SDIRK) techniques. In the latter case an iterated PISO-like procedure based on Rhie–Chow correction was used for handling pressure-velocity coupling within each RK stage. The accuracy of the considered algorithms was evaluated studying the Taylor–Green vortex. Moreover several benchmark solutions have been computed in order to assess the reliability, the accuracy and the robustness of the presented solvers.