Insertion of PETSc in the OpenFOAM Framework

OpenFOAM is a widely used open source framework for simulation in several areas of computational fluid dynamics and engineering. As a partial differential equation (PDE)-based framework, OpenFOAM suffers from a performance bottleneck in solving large-scale sparse linear systems of equations. To address the problem, this article proposes a novel OpenFOAM-PETSc framework by inserting PETSc, a dedicated numerical solving package, into the OpenFOAM to speed up the process of solving linear equation systems. The design of the OpenFOAM-PETSc framework is described, and the implementation of an efficient matrix conversion algorithm is given as a case study. Validation tests on a high-performance computing cluster show that OpenFOAM-PETSc reduces the time of solving PDEs by about 27% in the lid-driven cavity flow case and by more than 50% in flow around the cylinder case in comparison with OpenFOAM, without compromising the scalability. In addition, this article also gives a preliminary performance analysis of different numerical solution methods, which may provide guidelines for further optimizations.