Abstract
This paper presents a robust, efficient, and strongly scalable solution methodology for simulation of complex turbulent flows on unstructured grids. The compressible Reynolds averaged Navier–Stokes (RANS) equations and the negative Spalart–Allmaras (SA) turbulence model are discretized, in coupled form, using a Streamline Upwind Petrov–Galerkin (SUPG) scheme. The time integration is fully implicit, and the discretized equations are advanced towards a steady-state solution using a pseudo-transient continuation (PTC). For solution of the linearized systems, a preconditioned Krylov solver is used. Seeking robustness, Krylov solvers are commonly preconditioned using incomplete factorization methods such as ILU(k). However, these methods are neither memory efficient, nor strongly scalable. To provide a better alternative, the implicit line solution method, which has been traditionally used in finite-volume methods, is revised and enhanced to solve stiffer linear systems. In the developed method, the lines are generated using a matrix-based approach, which connects the strongly-coupled unknowns. In addition, to improve the robustness of the line solver for high-CFL systems, a dual-CFL strategy, with a lower CFL number in the preconditioner matrix, is developed. Also, it is shown that for high-order continuous finite-element discretizations, the interconnections of the degrees of freedom on a line form a banded matrix which is wider than tridiagonal, but still can be factorized completely without generating any fill-ins. The developed line preconditioner is strongly scalable and, in contrast to the ILU factorization, its convergence behavior does not depend on the number of partitions. Two three-dimensional numerical examples are presented in which the performance of the line preconditioner is compared with that of the ILU(k) preconditioner. This comparison shows that, in addition to robustness improvements, the line preconditioner offers significant benefits in terms of memory efficiency.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.