Papers by Behzad Reza Ahrabi
The objective of the present study is to investigate and develop robust, efficient, and scalable ... more The objective of the present study is to investigate and develop robust, efficient, and scalable multilevel solution strategies and preconditioning techniques for stabilized finite-element flow solvers. The proposed solution strategy is essentially a p-multigrid approach in which the solution on the mesh with lowest polynomial degree (p=1) is solved using a preconditioned Newton-Krylov method. Seeking robustness, the Newton-Krylov methods are commonly preconditioned using incomplete factorization methods such as ILU(k). However, it is well known that these methods are not scalable. To overcome this problem, we have developed an implicit line preconditioner which can be properly distrusted among processing elements, without affecting the convergence behavior of the linear system and the non-linear path. The lines are extracted from a stiffness matrix based on strong connections. To improve the robustness of the implicit-line relaxation, a dual CFL strategy, with a lower CFL number in the preconditioner matrix, has been developed. In this study, we also employ an algebraic multigrid (AMG) preconditioner and augment it with the dual-CFL strategy. To reach high-order discretizations, a set of hierarchical basis functions are employed and a non-linear p-multigrid approach is developed. In order to test the performance of the newly developed algorithms, a new flow solver for two and three dimensional mixed-element unstructured meshes has been developed in which the Reynolds averaged Navier-Stokes (RANS) equations and negative Spalart-Almaras (SA) turbulence model are discretized, in a coupled form, using the Streamline Upwind Petrov-Galerkin (SUPG) scheme. Several two-and three-dimensional numerical examples including turbulent flows over the 30P30N three element airfoil and a wing-body-tail configuration from the 4th AIAA Drag Prediction Workshop are presented in which the performance of the implicit line relaxation and algebraic multigrid preconditioners are compared with the incomplete lower upper factorization (ILU(k)) method. Results show positive steps toward development of scalable solution techniques.
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Papers by Behzad Reza Ahrabi