Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes

Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms

The Tera Multithreaded Architecture and Unstructured Meshes

The Tera Multithreaded Architecture (MTA) is a new parallel supercomputer currently being installed at San Diego Supercomputing Center (SDSC). This machine has an architecture quite different from contemporary parallel machines. The computational processor is a custom design and the machine uses hardware to support very fine grained multithreading. The main memory is shared, hardware randomized and flat. These features make the machine highly suited to the execution of unstructured mesh problems, which are difficult to parallelize on other architectures. We report the results of a study carried out during July-August 1998 to evaluate the execution of EUL3D, a code that solves the Euler equations on an unstructured mesh, on the 2 processor Tera MTA at SDSC. Our investigation shows that parallelization of an unstructured code is extremely easy on the Tera. We were able to get an existing parallel code (designed for a shared memory machine), running on the Tera by changing only the compiler directives. Furthermore, a serial version of this code was compiled to run in parallel on the Tera by judicious use of directives to invoke the "full/empty" tag bits of the machine to obtain synchronization. This version achieves 212 and 406 Mflop/s on one and two processors respectively, and requires no attention to partitioning or placement of data issues that would be of paramount importance in other parallel architectures

High Resolution Aerospace Applications using the NASA Columbia Supercomputer

This paper focuses on the parallel performance of two high-performance aerodynamic simulation packages on the newly installed NASA Columbia supercomputer. These packages include both a high-fidelity, unstructured, Reynolds-averaged Navier-Stokes solver, and a fully-automated inviscid flow package for cut-cell Cartesian grids. The complementary combination of these two simulation codes enables high-fidelity characterization of aerospace vehicle design performance over the entire flight envelope through extensive parametric analysis and detailed simulation of critical regions of the flight envelope. Both packages. are industrial-level codes designed for complex geometry and incorpor.ats. CuStomized multigrid solution algorithms. The performance of these codes on Columbia is examined using both MPI and OpenMP and using both the NUMAlink and InfiniBand interconnect fabrics. Numerical results demonstrate good scalability on up to 2016 CPUs using the NUMAIink4 interconnect, with measured computational rates in the vicinity of 3 TFLOP/s, while InfiniBand showed some performance degradation at high CPU counts, particularly with multigrid. Nonetheless, the results are encouraging enough to indicate that larger test cases using combined MPI/OpenMP communication should scale well on even more processors

CU++ET: An Object Oriented Tool for Accelerating Computational Fluid Dynamics Codes using Graphical Processing Units

The application of graphical processing units (GPU) to solve partial differential equations is gaining popularity with the advent of improved computer hardware. Various lower level interfaces exist that allow the user to access GPU specific functions. One such interface is NVIDIA's Compute Unified Device Architecture (CUDA) library. CUDA has been applied previously to solve the Three-Dimensional Euler equations, and a speed-up of the order of 500 has been reported in literature using multiple GPU units. However, porting existing codes to run on the GPU requires the user to write kernels that execute on multiple cores, in the form of Single Instruction Multiple Data (SIMD). In the present work, a higher level framework has been developed that uses object oriented programming techniques available in C++ such as polymorphism, operator overloading, and template meta programming. Using this approach, CUDA kernels can be generated automatically during compile time. Briefly, CU++ET allows a code developer with just C/C++ knowledge to write computer programs that will execute on the GPU without any knowledge of specific programming techniques in CUDA. It allows the user to reuse existing C/C++ CFD codes with minimal changes. This approach is tremendously beneficial for CFD code development because it mitigates the necessity of creating hundreds of GPU kernels for various purposes. In its current form, CU++ET provides a framework for parallel array arithmetic, simplified data structures to interface with the GPU, and smart array indexing. Using this framework, a higher-order 3D Euler solver (ARC3D-GPU) has been developed with a performance improvement of about 70x on a single GPU compared to traditional FORTRAN/CPU execution. An implementation of heterogeneous parallelism, i.e., utilizing multiple GPUs to simultaneously process a partitioned grid system with communication at the interfaces using MPI has been developed and tested. An unstructured version of CU++ET is also demonstrated with its application towards solving the incompressible Navier-Stokes equations

Comparison of NTF Experimental Data with CFD Predictions from the Third AIAA CFD Drag Prediction Workshop

Recently acquired experimental data for the DLR-F6 wing-body transonic transport con figuration from the National Transonic Facility (NTF) are compared with the database of computational fluid dynamics (CFD) predictions generated for the Third AIAA CFD Drag Prediction Workshop (DPW-III). The NTF data were collected after the DPW-III, which was conducted with blind test cases. These data include both absolute drag levels and increments associated with this wing-body geometry. The baseline DLR-F6 wing-body geometry is also augmented with a side-of-body fairing which eliminates the flow separation in this juncture region. A comparison between computed and experimentally observed sizes of the side-of-body flow-separation bubble is included. The CFD results for the drag polars and separation bubble sizes are computed on grids which represent current engineering best practices for drag predictions. In addition to these data, a more rigorous attempt to predict absolute drag at the design point is provided. Here, a series of three grid densities are utilized to establish an asymptotic trend of computed drag with respect to grid convergence. This trend is then extrapolated to estimate a grid-converged absolute drag level