Dmitri Sharov

IMPLEMENTATION OF UNSTRUCTURED GRID GMRES+LU-SGS METHOD ON SHARED-MEMORY, CACHE-BASED PARALLEL COMPUTERS

The implementation of an unstructured grid matrix-free GMRES+LU-SGS scheme on shared-memory, cache-based parallel machines is described. A special grid renumbering technique is used for the parallelization rather than the traditional method of partitioning the computational domain. The renumbering technique helps to avoid inter-processor data dependencies, cache-misses, and cache-line overwrite while allowing pipelining. The resulting source code can be used with maximum efficiency and without modifications on traditional (scalar) computers, vector supercomputers, and shared-memory parallel systems. Special attention has been paid to develop an optimally parallelized preconditioner for the GMRES scheme.

On the Computation of Compressible Turbulent Flows on Unstructured Grids

An accurate, fast, matrix-free implicit method has been developed to solve compressible turbulent How problems using the Spalart and Allmaras one equation turbulence model on unstructured meshes. The mean-flow and turbulence-model equations are decoupled in the time integration in order to facilitate the incorporation of different turbulence models and reduce memory requirements. Both mean flow and turbulent equations are integrated in time using a linearized implicit scheme. A recently developed, fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hybrid finite volume and finite element method, where the finite volume approximation based on a containment dual control volume rather than the more popular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux terms. The developed method is used to compute a variety of turbulent flow problems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method provides an accurate, fast, and robust algorithm for computing compressible turbulent flows on unstructured meshes.

PARALLEL UNSTRUCTURED GRID GMRES+LU-SGS METHOD FOR TURBULENT FLOWS

A parallel, mat,rix-free implicit GMRES+LUSGS method is presented on shared-memory, cachebased parallel computers using OpenMP for computing compressible turbulent flow problems. A special grid renumbering technique is used to achieve the parallelization rather than the traditional method of partitioning the computational domain. This renumbering technique helps to avoid inter-processor data dependencies, cache-misses, and cache-line overwrite while allowing pipelining. The resulting code can be used with maximum efficiency and without modifications on traditional scalar computers, vector supercomputers, and shared-memory parallel systems. The developed parallel implicit method has been used to predict drag forces in the transonic regime for both DLR.-F4 and DLR-F6 configurations. The numerical results in terms of parallel efficiency indicate that the present implicit method scales reasonably well and is suitable for computing turbulent flows for complex geometries. It is demonstrated that turnaround in a matter of hours for numerical simulation of high Reynolds number turbulent flows past realistic geometries has been achieved.

A Class of Matrix-Free Implicit Methods for Compressible Flows on Unstructured Grids

In recent years, significant progress has been made in developing numerical algorithms for the solution of the compressible Euler and Navier-Stokes equations on unstructured grids. Early efforts in the development of temporal discretization methods using unstructured grids, focused on the explicit schemes. In general, explicit temporal discretization methods such as multi-stage Runge-Kutta schemes and their boundary conditions are easy to implement, vectorize and parallelize, and require only limited memory storage. However, for large-scale problems and especially for the solution of the Navier-Stokes equations, the rate of convergence slows down dramatically, resulting in inefficient solution techniques. In order to speed up convergence, a multigrid strategy or an implicit temporal discretization is required. In general, implicit methods can outperform their explicit counterparts by a factor of 10 or even more. Unfortunately, this performance is usually achieved at the expense of memory increment, as some efficient implicit methods might need up to an order of magnitude more storage than the explicit methods. This is mainly due to the fact that implicit methods usually require the computation of the left-hand-side Jacobian matrix in addition to construction of the right-hand-side residual. The storage of the Jacobian matrix consumes an enormous amount of memory, which may be prohibitive for large scale problems.

Recent Developments of a Coupled CFD/CSD Methodology

A recently developed loose-coupling algorithm that combines state-of-the-art Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies has been applied to the simulations of weapon-structure interactions. The coupled methodology enables cost-effective simulation of fluid-structure interactions with a particular emphasis on detonation and shock interaction. The coupling incorporates two codes representing the state-of-the-art in their respective areas: FEFLO98 for the Computational Fluid Dynamics and DYNA3D for the Computational Structural Dynamics simulation. An application of the methodology to a case of weapon detonation and fragmentation is presented, as well as fragment and airblast interaction with a steel wall. Finally, we present results of simulating airblast interaction with a reinforced concrete wall, in which concrete and steel rebar failure and concrete break-up to thousands of chunks and dust particles are demonstrated.

Time-Accurate Implicit ALE Algorithm for Shared-Memory Parallel Computers

An unstructured grid matrix-free GMRES+LU-SGS scheme is used to simulate unsteady CFD problems with moving bodies. The method is applied on sharedmemory, cache-based parallel machines. A special grid renumbering technique is used for the parallelization rather than the traditional method of partitioning the computational domain. Moving mesh with recurrent remeshing models the body motion.

AN OVERLAPPING UNSTRUCTURED GRID METHOD FOR VISCOUS FLOWS

An overlapping unstructured grid method has been developed to solve compressible turbulent flow problems using one equation turbulence model. The idea behind this is to combine the advantages of both overlapping and unstructured grids in an effort to develop a more efficient, robust, and user-friendly method for solving high Reynolds number viscous flow problems around complex geometries. In this method, an anisotropic unstructured grid is independently generated for each component of a given configuration, and an isotropic unstructured grid is then generated to cover the whole computational domain. The developed method is applied to compute a variety of high Reynolds number flow problems. The numerical results obtained indicate that the present method provides an accurate, viable, robust, and user-friendly approach for computing viscous flows.