Unstructured Grid Generation Techniques and Software

The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop

Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

Development of an Unsteady Aeroelastic Solver for the Analysis of Modern Turbomachinery Designs

Developers of aircraft gas turbine engines continually strive for greater efficiency and higher thrust-to-weight ratio designs. To meet these goals, advanced designs generally feature thin, low aspect airfoils, which offer increased performance but are highly susceptible to flow-induced vibrations. As a result, High Cycle Fatigue (HCF) has become a universal problem throughout the gas turbine industry and unsteady aeroelastic computational models are needed to predict and prevent these problems in modern turbomachinery designs. This research presents the development of a 3D unsteady aeroelastic solver for turbomachinery applications. To accomplish this, a well established turbomachinery Computational Fluid Dynamics (CFD) code called Corsair is loosely coupled to the commercial Computational Structural Solver (CSD) Ansys® through the use of a Fluid Structure Interaction (FSI) module. Significant modifications are made to Corsair to handle the integration of the FSI module and improve overall performance. To properly account for fluid grid deformations dictated by the FSI module, temporal based coordinate transformation metrics are incorporated into Corsair. Wall functions with user specified surface roughness are also added to reduce fluid grid density requirements near solid surfaces. To increase overall performance and ease of future modifications to the source code, Corsair is rewritten in Fortran 90 with an emphasis on reducing memory usage and improving source code readability and structure. As part of this effort, the shared memory data structure of Corsair is replaced with a distributed model. Domain decomposition of individual grids in the radial direction is also incorporated into Corsair for additional parallelization, along with a utility to automate this process in an optimal manner based on user input. This additional parallelization helps offset the inability to use the fine grain mp-threads parallelization in the original code on non-distributed memory architectures such as the PC Beowulf cluster used for this research. Conversion routines and utilities are created to handle differences in grid formats between Corsair and the FSI module. The resulting aeroelastic solver is tested using two simplified configurations. First, the well understood case of a flexible cylinder in cross flow is studied with the natural frequency of the cylinder set to the shedding frequency of the Von Karman streets. The cylinder is self excited and thus demonstrates the correct exchange of energy between the fluid and structural models. The second test case is based on the fourth standard configuration and demonstrates the ability of the solver to predict the dominant vibrational modes of an aeroelastic turbomachinery blade. For this case, a single blade from the fourth standard configuration is subjected to a step function from zero loading to the converged flow solution loading in order to excite the structural modes of the blade. These modes are then compared to those obtained from an in vacuo Ansys® analysis with good agreement between the two

Automatic parallel octree grid generation software with an extensible solver framework and a focus on urban simulation

The development of an automatic, dynamic, parallel, Cartesian, linear forest-of-octree grid generator and partial differential equation (PDE) solver framework is presented. This research is bundled into an application programmed with C++ which uses MPI for distributed parallelism. The application is named paros which stands for PARallel Octree Solver. In its current implementation, the application provides a \u27zeroth\u27 order representation of the target geometry, and as such, no cut-cell algorithm, projection method, or immersed boundary condition are implemented. In this case, \u27zeroth\u27 order means that no geometry is ever exactly represented in the final computational mesh: an octree element is either completely in the domain or entirely outside of it. Any element that contains or is intersected by a geometry facet is removed from the final mesh which results in a \u27blocky\u27 or \u27stepped\u27 geometry representation and simplifies boundary computations. The computational octree mesh creation is completely parallel and automated. The algorithm is dynamic in the sense that it is repartitioned dynamically throughout the grid generation process to maintain optimal load balancing during all phases of the mesh genesis. A linear octree data structure is used to store the octree mesh elements and is leveraged for optimal load balancing. An additional hierarchical octree is used to significantly improve algorithms that suffer from this linear storage paradigm. This work focuses on, but is not limited to, applications related to urban simulations and may be applied to plume/contaminant propagation. Within the PDE solution framework a cell-centered, incompressible, unsteady, Navier Stokes solver with an energy term to account for thermal buoyancy is implemented and validated using canonical test cases. Turbulence closure is implemented in the form of the Smagorinski large eddy simulation (LES) model. The parallel grid generation and solution process is tested on a large scale cityscape geometry and shown to be robust and efficient. Additionally, an implementation of the compressible Navier-Stokes equations is coded within the framework. The framework is extensible such that adding other types of numerical PDE solvers should not be difficult. Other features including adaptive mesh refinement (AMR) and contaminant transport functionality are included