Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems

This dissertation develops the lattice Boltzmann method (LBM) as a strong alternative to traditional numerical methods for solving incompressible fluid flow problems. The LBM outperforms traditional methods on a standalone basis for certain problem cases while for other cases it can be coupled with the traditional methods using domain decomposition. This brings about a composite numerical scheme which associates the efficient numerical attributes of each individual method in the composite scheme with a particular region in the flow domain. Coupled lattice Boltzmann-traditional finite difference procedures are developed and evaluated for CPU time reduction and accuracy of standard test cases. The standard test cases are numerical solutions of the two-dimensional unsteady and steady convection-diffusion equations and two-dimensional steady laminar incompressible flows represented by the backward-facing step flow problem and the flow problem around a cylinder. Multiblock Cartesian grids and hybrid Cartesian-cylindrical grid systems are employed with the composite numerical scheme. A cache-optimized lattice Boltzmann technique is developed to utilize the full computational strength of the LBM. The LBM is an explicit time-marching method and therefore has a time step size limitation. The time step size is limited by the grid spacing and the Mach number. A lattice Boltzmann simulation necessarily requires a low Mach number since it relates to the incompressible Navier-Stokes equations in the low Mach number limit. For steady state problems, the smaller time step results in slow convergence. To improve the time step limitation imposed by the grid spacing, an improved LBM that adopts a new numerical discretization for the advection term has been developed and the results were computed for a convection-diffusion equation and compared with the original LBM. The performance of traditional finite difference methods based on the alternating direction implicit scheme for the convection-diffusion equation and the vorticity-stream function method for the laminar incompressible flow problems is evaluated against the composite numerical scheme. The composite numerical scheme is shown to take lesser CPU time for solving the given benchmark problems

Parallel unstructured solvers for linear partial differential equations

This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested

Parallel Aerodynamic Simulation on Open Workstation Clusters. Department of Aerospace Engineering Report no. 9830

The parallel execution of an aerodynamic simulation code on a non-dedicated, heterogeneous cluster of workstations is examined. This type of facility is commonly available to CFD developers and users in academia, industry and government laboratories and is attractive in terms of cost for CFD simulations. However, practical considerations appear at present to be discouraging widespread adoption of this technology. The main obstacles to achieving an efficient, robust parallel CFD capability in a demanding multi-user environment are investigated. A static load-balancing method, which takes account of varying processor speeds, is described. A dynamic re-allocation method to account for varying processor loads has been developed. Use of proprietary management software has facilitated the implementation of the method

Parallel unstructured solvers for linear partial differential equations

This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

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

Extension of a 2D Multiblock Structured Overset Suite to a Fully 3D Multiblock Unstructured Flow Solver

RÉSUMÉ Ce présent mémoire illustre les récents développements apportés aux logiciels chimères du laboratoire de recherche du professeur Éric Laurendeau à Polytechnique Montréal. Dans la dynamique des fluides numériques mieux connue en anglais sous le nom de « Computa- tional Fluid Dynamics » (CFD), les méthodes chimères aussi connues en anglais sous le nom d’« overset » permettent de faire des simulations multigéométries complexes sans lesquelles le processus de génération de maillages pourrait être très compliqué, soit même impossible. Essentiellement, ces méthodes permettent de lier et d’assembler des maillages individuels con- tenant chacun différentes géométries en un seul par le biais d’interpolations et d’interfaces. Ceci permet de grandement réduire le temps à générer des maillages, car ces derniers peuvent être générés individuellement. Conséquemment, cela permet de passer plus de temps à exé- cuter des simulations ou même implémenter de nouvelles fonctionnalités au sein de solveurs de CFD, ce qui est très utile dans un environnement de travail industriel et de recherche. Pour que les méthodes chimères fonctionnent, il est nécessaire d’effectuer quelques étapes au niveau du préprocesseur d’un solveur de CFD. Cela normalement inclut un processus de découpage, un algorithme de recherche de paires de cellules donneuses et interpolées, et un algorithme d’interpolation. Une fois que ces étapes sont complétées, la simulation peut ensuite être effectuée. Dans le cadre de ce laboratoire de recherche, la présente implémentation 2D a certains prob- lèmes connus non résolus. Également, ces méthodes 2D sont difficilement transférables à des applications 3D lors des transferts technologiques avec l’industrie qui se servent de solveurs de CFD 3D à topologies structurée et non structurée. La partie 2D de ce mémoire concerne les solutions aux problèmes au sein du préprocesseur chimère de NSCODE qui est un solveur de CFD 2D structuré. Plusieurs problèmes avec les méthodes implémentées dans le passé ont été identifiés et résolus dans le cadre de ce mémoire. Le premier problème concerne les erreurs de décalage avec les poids d’interpolation qui sont calculés aux nœuds des cellules au lieu d’être calculés au centre des cellules. Un nouveau schéma d’interpolation est mis en place dans lequel la précision et la fidélité du schéma précédent sont retenues tout en calculant les poids d’interpolation au centre des cellules. Le deuxième problème concernait la difficulté à générer des maillages de type «collar» qui sont un type particulier de maillages qui présentent une discrétisation plus fine de la géométrie pour un endroit en particulier du maillage d’arrière-plan. Des améliorations à NSGRID qui est le mailleur 2D structuré du laboratoire de recherche ont été effectuées.----------ABSTRACT The present thesis addresses the recent developments made to the overset framework of Pro- fessor Éric Laurendeau’s research lab at Polytechnique Montreal. In Computational Fluid Dynamics (CFD), overset methods allow complex multi-geometry simulations for which with- out its use the meshing process can be tedious, if not impossible. Essentially, these methods link individual meshes containing different geometries together by the means of interpola- tion and interfaces. This reduces the time spent on meshing since elements of the geometry can be meshed out individually, and thus more time can be spent on running simulations or implementing new features in a CFD flow solver which is a highly valuable resource in a research/industrial environment. In order for overset methods to work, a couple of steps are taken at the preprocessor level of the CFD flow solver in question. They usually include a hole cutting process, a donor search algorithm, and an interpolation algorithm. Once these steps are done, the simulation can then be performed. In the case of this research lab, the current framework has some pitfalls with its 2D imple- mentation and the ability of its methods to be used for 3D applications in the case of doing technological transfers with the industry who use both 3D CFD flow solvers with structured and unstructured topology. The 2D part of this thesis concerns the solutions to the problems inside the overset prepro- cessor of NSCODE which is a 2D structured CFD flow solver. Several problems with the methods implemented in the past have been identified and are solved in the case of this thesis. The first problem concerns offset errors with the interpolation weights calculated at the cell vertices instead of the cell centers. A new interpolation scheme is devised in which the pre- cision and accuracy of the first one are retained while having the weights properly calculated at the cell centers. The second issue was with the rigidity of generating collar grids which is a type of mesh that possesses a finer discretization of the geometry for a specified region of the background mesh. Improvements to NSGRID which is the 2D structured mesher of the research lab have been made in that regard. Users can now generate normally projected collar grids with easier inputs. The third issue concerns the solid-solid discontinuity problem that occurs when 2 overset meshes share the same solid geometry (i.e. a collar grid with a background mesh). The results demonstrate the geometric correction that is employed to recreate halo cells which are cells found on the fringes of the mesh. In the case of the overset method, these cells are necessary for proper computation of derived values such as the pressure coefficient and coefficient of friction