Development of low-dissipative projection method framework integrating various high-order time integration schemes using OpenFOAM

Abstract

A low-dissipative solution framework integrating various types of high-order time scheme is proposed and implemented based on the open-source C++ library OpenFOAM. This framework aims to introduce different categories of low-dissipative time integration schemes into a unified solver convenient for comparison of scheme performance in finite volume computational fluid dynamics code, contributing to the development of low dissipation scheme appropriate for scale-resolving turbulence simulation. To demonstrate this general framework's ability of including a wide range of time integration method, in addition to typical Runge--Kutta family schemes of linear single-step method, two more complex linear multi-step method, Adams--Bashforth family and Adams--Bashforth--Moutton family schemes, are implemented with the projection algorithm, which increase the options of time discretization. The unified solver obtained by the solution framework select the specified time scheme from a variety of alternatives in runtime rather than maintaining multiple solvers with each compiled for a single scheme, while new scheme can be easily added according to the basic idea of this universal framework. Further research on the stability of the explicit scheme indicates that a multi-step method with an appropriate order may be an optimal choice when taking both the prediction accuracy and computational efficiency into account in unstable problems.