Implementation of density-based implicit LU-SGS solver in the framework of OpenFOAM

• Implicit steady and dual-time LU-SGS solver is implemented in OpenFOAM.
• The implementation codes of the sweep process in LU-SGS approach are introduced.
• Typical test cases are used to investigate the performance of LU-SGS solver.
• Convergence performance of LU-SGS solver is superior to original explicit solver.
• The LU-SGS solver is significantly more efficient than original explicit solver.

In this paper, in the framework of OpenFOAM, the density-based steady and unsteady dual-time implicit LU-SGS solvers which are termed as lusgsFoam and lusgsDualFoam are established. The key implementation details of the forward and backward sweep looping process in the LU-SGS approach are introduced. Three typical test cases, i.e. hypersonic airflow across cylinder(steady), subsonic flow over bump (steady) and supersonic forward step flow (unsteady), are used to investigate the performance of these LU-SGS solvers, and the density-based explicit solver, i.e. the rhoCentralFoam in the official OpenFOAM, is adopted as the comparison solver. Through the comparison of the numerical results for the first two steady cases, it is found that, the convergence performance of the LU-SGS solver is significantly superior to explicit solver rhoCentralFoam. Meanwhile, considering the combined effect of time step and the iteration efficiency, the LU-SGS solver, lusgsFoam is significantly more efficient than the explicit solver, rhoCentralFoam. For the third test case, i.e. the unsteady supersonic forward step flow, the spatial accuracy of the unsteady dual time lusgsDualFoam solver is a little lower than the explicit rhoCentralFoam, but overall, this unsteady implicit solver can capture the transient characteristics efficiently.