An investigation of parallel implicit solution algorithms for incompressible flows on multielement unstructured topologies

The primary objective of this study is to develop an efficient incompressible flow solver capable of performing viscous, high Reynolds number flow simulations for complex geometries using general unstructured grids. This parallel flow solver is demonstrated for large-scale meshes with viscous sublayer resolution (p+ N 1) and approximately lo6 points or more. Primary issues addressed in this work are 1) treatment of the connectivity between subdomain interfaces, 2) proper definition of the iteration hierarchy, and 3) methods for coupling of subdomains. The present parallel unstructured viscous flow solver is based on a domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solution algorithm employs iterative solution of the implicit approximation, with coupling between subdomains according to several schemes that are a primary focus of the study. MPI message passing is used for interprocessor communication. Applications include 1) a full-scale ship hull, 2) the SUBOFF model hull with stern appendages, and 3) a fully-configured high-lift transport. Introduction Implicit algorithms for flows on unstructured grids have been investigated extensively by a variety of authors [l] [2] [3] [4]. However, implicit algorithms are much more difficult to) parallelize, because of their inherent global dependencies. As such, the parallelization of unstructured Euler solvers [5] [S] [7] and Navier-Stokes solvers [S] [9] [lo] have been previously investigated. This work seeks to examine a relaxation-type algorithm *Research Assistant I, Member ASME *Research Engineer I, Member AIAA SProfessor, Member AIAA §Distinguished Professor, Member AIAA Copyright@2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. in depth to provide insight concerning issues that arise in the parallelization of implicit solution algorithms on unstructured topologies. In general, the parallelization of an existing validated flow solver should satisfy several constraints. First and most important; the accuracy of the overall numerical scheme must not be compromised; i.e., the solution computed in parallel must have a oneto-one correspondence with the solution computed in serial mode. Also, the code must be efficient irrits use of computational resources. This characteristic is measured in terms of memory usage and scalability, as well as the fact that the parallel code should degenerate to the serial version if only one processor is available. Finally, the consequences of the inevitable domain decomposition should not seriously compromise the convergence rate of the iterative,algorithm. The present parallel unstructured viscous flow solver is based on a coarse-grained domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solver also has the capability to map an arbitrary number of subdomains to a physical processor; thus, some flexibility is available to leverage available memory should memory resources be scarce. The present solution algorithm is related to several previous efforts. The approach is an evolution of the implicit flow solver and code of Anderson et al. [ll] [12] [13]; the solver developed in this series of works demonstrates 3D, implicit, high Reynolds number solution capability. Also, this work follows the unstructured multiblock solver of Sheng and Whitfield [14] [15] which uses the same core solver but employs a multiblock technique to reduce memory consumption by 70%. These studies are in turn related to the multiblock structured solvers originating from Taylor, Whitfield, and Sheng [16] [17] [18]. Elements of the present approach to parallel solution are related to the parallel multiblock structured grid solver of Pankajakshan and Briley [19].