Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines

Two renumbering strategies for field solvers based on unstructured grids that operate on shared-memory, cache-based parallel machines are described. Special attention is paid to the avoidance of cache-line overwrite, which can lead to drastic performance degradation on this type of machines. Both renumbering techniques avoid cache-misses and cache-line overwrite while allowing pipelining, leading to optimal coding for this type of hardwar

Graphics hardware acceleration for rotorcraft simulations

Interest in scientific programming using graphics processing units (GPUs) has exploded in recent years. The advent of NVIDIA\u27s CUDA programming language in early 2007 enabled GPU acceleration of numerical software to become mainstream. Relative to central processing units (CPUs), these devices have extremely high floating point operation capability and memory bandwidth. Combined with relatively low cost, they are attractive alternatives to more expensive traditional supercomputers. Porting existing computational fluid dynamics methods to the new hardware is not always straightforward. Modern GPUs are massively parallel, some consisting of over 400 processors, utilizing a unique hierarchy of computational units and memory management. Fully exploiting this architecture for CFD solvers requires the development of new algorithms tailored to the devices. To that end, this work presents a solution method for the Navier-Stokes equations using the SIMPLER algorithm on structured Cartesian grids. A block-iterative scheme with a parallel recursive tridiagonal solver is used for the discretized equations, giving considerable performance advantages over prior point-iterative implementations. Using a $200 GPU in a standard workstation, accelerations of over 20x are observed compared to a serial CPU implementation for rotorcraft simulations

Parallel surface reconstruction through virtual milling

Surface definition deals with representing a surface analytically using a finite number of parameters and with acceptable levels of error. In the past few years it has become a key discipline in Computational Fluid Dynamics (CFD). Recent advances in computers and numerical algorithms have made it possible for CFD practitioners to attempt flow solutions about complex three-dimensional geometries. The first step in this process is having a numerical representation of the shape. In many cases of interest such a representation already exists; i.e., aircraft designed on a computer. Such Computer-Aided Design (CAD) descriptions do not exist, though, for objects found in nature or predating CAD. In such situations a technique for measuring the object and then constructing a surface conforming to these measurements is needed;Existing techniques for 3-D surface definition often require considerable human intervention, both in the measuring and the reconstruction process. This is a time consuming proposition. It is desirable to develop a fully automated alternative;Three-dimensional objects can be measured accurately and quickly from multiple viewpoints using a Cyberware laser digitizer. The digitizer returns the coordinates of a set of surface points. The problem is then to construct a faithful representation of the original object from these points. The algorithm proposed here has two distinct stages. In the first stage, surface fragments, using information from a single view, are produced by employing a visibility constraint and a 2-D Delaunay triangulation technique. In the next stage, surfaces from multiple views are combined through an approach that emulates the machining operation of milling. The final result is a non-convex, triangular faceted, polyhedron that approximates the object shape;A sequential version of the virtual milling algorithm exists on a Silicon Graphics workstation. The algorithm is of O(NlogN) complexity, where N is the number of data points. Experimental results have been obtained for a scaled F117-A model scanned from multiple viewpoints. Several topological issues have been addressed;A parallel version of the algorithm has been implemented on the Intel Gamma Prototype, a 128 node, distributed-memory, MIMD computer. Run times are compared to those obtained on an Iris 310/VGX workstation

Unstructured grid algorithms for two- and three-dimensional flows on parallel computers

The Navier-Stokes equations are solved numerically for two-and three-dimensional viscous laminar flows. The domain is discretized using triangular control volumes in two dimensions and tetrahedra in three dimensions, using existing grid generators. The flow solvers are implemented on a variety of computers, including distributed memory parallel computers;A finite-volume approach is used to discretize the governing flow equations in conservation law form using conserved variables. A cell centered approach is used where the unknowns are computed at the center of each control volume. Both explicit and implicit solution strategies are pursued. In the two-dimensional version of the algorithm an explicit upwind scheme as well as a central-difference scheme with added artificial dissipation is used. The upwind scheme implemented in two dimensions is the advection upstream splitting method. Time-derivative preconditioning using primitive and conserved variables is applied to the two-dimensional flow solver. Time-derivative preconditioning is used to enhance the low Mach number rate of convergence. A multistage Runge-Kutta scheme is used to advance the solution in time;In the three-dimensional version of the algorithm, an implicit upwind scheme is used. For the implicit scheme, an approximate flux Jacobian is used on the left hand side to reduce the computational effort and a Roe flux difference splitting is used on the right hand side. The gradients in the control volume need to be computed so the upwind scheme is second order accurate;The gradients in each cell are computed based on the values of the flow variables at the vertices of the grid. The values at the vertices of the grid are obtained by inverse distance weighting all the cell-centered values of the control volumes surrounding each vertex. For the implicit scheme, a block Gauss-Seidel solver is used to solve the resulting sparse matrix. The correctness of the solution strategies is determined by comparing the calculated solutions to data available in the literature;The schemes are implemented on parallel distributed memory computers. The parallelism exploited is coarse grained. The discretized solution domain is partitioned such that each processing unit is allocated a part of the domain. The processing units perform the solution of the Navier-Stokes equations independently from each other on different parts of the grid and with different data. Communication between processors is needed to properly model the domain;Numerical results for two-dimensional flows are obtained for a developing channel flow, a sudden expansion flow, a driven cavity flow with and without heat transfer and the flow over on obstruction in a channel. Three-dimensional flows computed are a developing straight channel flow of constant cross section, a driven cavity flow, and a developing curved channel flow. Good agreement of the computed results with data available in the literature is found

An algorithm for parallel unstructured mesh generation and flow analysis

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1996.Includes bibliographical references (p. 113-119).by Tolulope O. Okusanya.M.S

High order resolution and parallel implementation on unstructured grids

The numerical solution of the two-dimensional inviscid Euler flow equations is given. The unstructured mesh is generated by the advancing front technique. A cell-centred upwind finite volume method has been adopted to discretize the Euler equations. Both explicit and point implicit time stepping algorithms are derived. The flux calculation using Roe's and Osher's approximate Riemann solvers are studied. It is shown that both the Roe and Osher's schemes produce an accurate representation of discontinuities (e.g. shock wave). It is also shown that better convergence performance has been achieved by the point implicit scheme than that by the explicit scheme. Validations have been done for subsonic and transonic flow over airfoils, supersonic flow past a compression corner and hypersonic flow past cylinder and blunt body geometries. An adaptive remeshing procedure is also applied to the numerical solution with the objective of getting improved results. The issue of high order reconstruction on unstructured grids has been discussed. The methodology of the Taylor series expansion is adopted. The calculation of the gradient at a reference point is carried out by the use of either the Green-Gauss integral formula or the least-square methods. Some recently developed limiter construction methods have been used and their performance has been demonstrated using the test example of the transonic flow over a RAE 2822 airfoil. It has been shown that similar pressure distributions are obtained by all limiters except for shock wave regions where the limiter is active. The convergence problem is illustrated by the mid-mod type limiter. It seems only the Venkatakrishnan limiter provides improved convergence. Other limiters do not appear to work as well as that shown in their original publications. Also the convergence history given by the least-square method appears better than that by the Green-Gauss method in the test

Computational Aerodynamics on unstructed meshes

New 2D and 3D unstructured-grid based flow solvers have been developed for simulating steady compressible flows for aerodynamic applications. The codes employ the full compressible Euler/Navier-Stokes equations. The Spalart-Al Imaras one equation turbulence model is used to model turbulence effects of flows. The spatial discretisation has been obtained using a cell-centred finite volume scheme on unstructured-grids, consisting of triangles in 2D and of tetrahedral and prismatic elements in 3D. The temporal discretisation has been obtained with an explicit multistage Runge-Kutta scheme. An "inflation" mesh generation technique is introduced to effectively reduce the difficulty in generating highly stretched 2D/3D viscous grids in regions near solid surfaces. The explicit flow method is accelerated by the use of a multigrid method with consideration of the high grid aspect ratio in viscous flow simulations. A solution mesh adaptation technique is incorporated to improve the overall accuracy of the 2D inviscid and viscous flow solutions. The 3D flow solvers are parallelised in a MIMD fashion aimed at a PC cluster system to reduce the computing time for aerodynamic applications. The numerical methods are first applied to several 2D inviscid flow cases, including subsonic flow in a bump channel, transonic flow around a NACA0012 airfoil and transonic flow around the RAE 2822 airfoil to validate the numerical algorithms. The rest of the 2D case studies concentrate on viscous flow simulations including laminar/turbulent flow over a flat plate, transonic turbulent flow over the RAE 2822 airfoil, and low speed turbulent flows in a turbine cascade with massive separations. The results are compared to experimental data to assess the accuracy of the method. The over resolved problem with mesh adaptation on viscous flow simulations is addressed with a two phase mesh reconstruction procedure. The solution convergence rate with the aspect ratio adaptive multigrid method and the direct connectivity based multigrid is assessed in several viscous turbulent flow simulations. Several 3D test cases are presented to validate the numerical algorithms for solving Euler/Navier-Stokes equations. Inviscid flow around the M6 wing airfoil is simulated on the tetrahedron based 3D flow solver with an upwind scheme and spatial second order finite volume method. The efficiency of the multigrid for inviscid flow simulations is examined. The efficiency of the parallelised 3D flow solver and the PC cluster system is assessed with simulations of the same case with different partitioning schemes. The present parallelised 3D flow solvers on the PC cluster system show satisfactory parallel computing performance. Turbulent flows over a flat plate are simulated with the tetrahedron based and prismatic based flow solver to validate the viscous term treatment. Next, simulation of turbulent flow over the M6 wing is carried out with the parallelised 3D flow solvers to demonstrate the overall accuracy of the algorithms and the efficiency of the multigrid method. The results show very good agreement with experimental data. A highly stretched and well-formed computational grid near the solid wall and wake regions is generated with the "inflation" method. The aspect ratio adaptive multigrid displayed a good acceleration rate. Finally, low speed flow around the NREL Phase 11 Wind turbine is simulated and the results are compared to the experimental data