DEVELOPMENT OF OPENFOAM SOLVERS FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS BASED ON HIGH-ORDER RUNGE-KUTTA SCHEMES

摘要

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.