incompressibleFoam: a new time consistent framework with BDF and DIRK integration schemes

TL;DR

This paper introduces incompressibleFoam, a new OpenFOAM solver integrating multiple numerical methods, including BDF and SDIRK time schemes, and compares its performance with existing solvers on benchmark cases.

Contribution

It presents a novel incompressible solver with integrated BDF and SDIRK schemes, and provides practical insights into numerical method choices within OpenFOAM.

Findings

CMI is preferable to pressure-corrected forms.

Third order schemes are not significantly better than second order.

Using CMI reduces dependence on time step and relaxation factors.

Abstract

This work focuses on the development of a new incompressible solver, incompressibleFoam, within OpenFOAM and integrating several numerical methods within the same framework. Two momentum interpolation (NCMI/CMI) methods are implemented, two forms of the pressure Poisson equation (corrected/standard). Regarding time discretization, steady-state, Backward Differentiation Formula (BDF) and the Singly Diagonally Implicit Runge-Kutta (SDIRK) methods, up to the third order, are implemented. The solver is tested on three benchmark cases to assess the performance of different numerical configurations. The results are also compared with the standard incompressible solver of OpenFOAM: pimpleFoam. They provide perspective on previous attempts to improve OpenFOAM incompressible solvers and give practical results regarding the choice of momentum interpolation methods, pressure equation formulations, and time discretization schemes. It is found that the pressure-corrected form should be avoided while using the NCMI and that third order schemes are not superior to 2nd order schemes. The CMI should be privileged to avoid time step and relaxation factor dependence and pressure velocity decoupling. Finally, the source code is released in the following github repository: https://github.com/ferrop/incompressibleFoam