An Improved Density-Based Compressible Flow Solver in OpenFOAM for Unsteady Flow Calculations

Abstract

OpenFOAM is a C++ programming language-based open-source platform for finite volume calculations in CFD. rhoCentralFoam is a density-based compressible flow solver widely used in the OpenFOAM community either directly for various kinds of flow solutions or for the development of other derived solvers for handling some specialized problems such as combustion, high enthalpy hypersonic flow simulations etc. The current implementation of rhoCentralFoam solver is second-order accurate in space but provides a stable solution with first-order time accurate scheme only. Moreover, rhoCentralFoam solver has been reported to breakdown for the solution of very low Mach number flows. In rhoCentralFoam, the governing equations are time-integrated sequentially resulting in numerical instabilities such as spurious oscillations even at low CFL numbers. To remedy this issue, the authors implement and demonstrate an improved solution technique, which time integrates the governing equations simultaneously for inviscid flow. The viscous solution is still obtained through an operator-splitting method as used in rhoCentralFoam. Implicit discretization of the corrector step ensures that there is no added restriction on time step for diffusion dominated flows due to high Peclet number. However, the maximum CFL number needs to be restricted to 1.0 due to the use of explicit time integration method. This improved algorithm is found to be highly stable without much numerical dissipation and can produce non-oscillatory solutions at a CFL number close to 1.0.