Performance Improvements of Krylov Subspace Methods in Numerical Heat Transfer and Fluid Flow Simulations

In recent years, advancements in computational hardware have enabled massive parallelism that can significantly reduce the duration of many numerical simulations. However, many high-fidelity simulations use serial algorithms to solve large systems of linear equations and are not well suited to exploit the parallelism of modern hardware. The Tri-Diagonal Matrix Algorithm (TDMA) is one such example of a serial algorithm that is ubiquitous in numerical simulations of heat transfer and fluid flow. Krylov subspace methods for solving linear systems, such as the Bi-Conjugate Gradients (BiCG) algorithm, can offer an ideal solution to improve the performance of numerical simulations as these methods can exploit the massive parallelism of modern hardware. In the present work, Krylov-based linear solvers of Bi-Conjugate Gradients (BCG), Generalized Minimum Residual (GMRES), and Bi-Conjugate Gradients Stabilized (BCGSTAB) have been incorporated into the SIMPLER algorithm to solve a three-dimensional Rayleigh-Bénard Convection model. The incompressible Navier-Stoke’s equations, along with the continuity and energy equations, are solved using the SIMPLER method. The computational duration and numerical accuracy for the Krylov-solvers are compared with that of the TDMA. The results show that Krylov methods can improve the speed of convergence for the SIMPLER method by factors up to 7.7 while maintaining equivalent numerical accuracy to the TDMA.