Several different time-integration algorithms for the Euler equations are investigated on two distributed-memory parallel computers using an explicit message-passing paradigm: these are classic Euler Explicit, four-stage Jameson-style Runge-Kutta, Block Jacobi, Block Gauss-Seidel, and Block Symmetric Gauss-Seidel. A finite-volume formulation is used for the spatial discretization of the physical domain. Both two- and three-dimensional test cases are evaluated against five reference solutions to demonstrate accuracy of the fundamental sequential algorithms. Different schemes for communicating or approximating data that are not available on the local compute node are discussed and it is shown that complete sharing of the evolving solution to the inner matrix problem at every iteration is faster than the other schemes considered. Speedup and efficiency issues pertaining to the various time-integration algorithms are then addressed for each system. Of the algorithms considered, Symmetric Block Gauss-Seidel has the overall best performance. It is also demonstrated that using parallel efficiency as the sole means of evaluating performance of an algorithm often leads to erroneous conclusions; the clock time needed to solve a problem is a much better indicator of algorithm performance. A general method for extending one-dimensional limiter formulations to the unstructured case is also discussed and applied to Van Albada’s limiter as well as Roe’s Superbee limiter. Solutions and convergence histories for a two-dimensional supersonic ramp problem using these limiters are presented along with computations using the limiters of Barth & Jesperson and Venkatakrishnan — the Van Albada limiter has performance similar to Venkatakrishnan’s. / Ph. D.

Within the design process, computational fluid dynamics is typically used to compute specific quantities that assess the performance of the apparatus under investigation. These quantities are usually integral output functions such as force and moment coefficients. However, to accurately model the configuration, the geometric features and the resulting physical phenomena must be adequately resolved. Due to limited computational resources a compromise must be made between the fidelity of the solution obtained and the available resources. This creates a degree of uncertainty about the error in the computed output functions. To this end, the current study attempts to address this problem for two-dimensional inviscid, incompressible flows on unstructured grids. The objective is to develop an error estimation and grid adaptive strategy for improving the accuracy of output functions from computational fluid dynamic codes. The present study employs a discrete adjoint formulation to arrive at the error estimates in which the global error in the output function is related to the local residual errors in the flow solution via adjoint variables as weighting functions. This procedure requires prolongation of the flow solution and adjoint solution from coarse to finer grids and, thus, different prolongation operators are studied to evaluate their influence on the accuracy of the error correction terms. Using this error correction procedure, two different adaptive strategies may be employed to enhance the accuracy of the chosen output to a prescribed tolerance. While both strategies strive to improve the accuracy of the computed output, the means by which the adaptation parameters are formed differ. The first strategy improves the computable error estimates by forming adaptation parameters based on the level of error in the computable error estimates. A grid adaptive scheme is then implemented that takes into account the error in both the primal and dual solutions. The second strategy uses the computable error estimates as indicators in an iterative grid adaptive scheme to generate grids that produce accurate estimates of the chosen output. Several test cases are provided to demonstrate the effectiveness and robustness of the error correction procedure and the grid adaptive methods.

The primary objective of this study is to develop a sliding interface method for simulations involving relative rotational grid motion suitable for unstructured grid topologies. The present method alleviates computationally expensive grid deformation, remeshing, and hole cutting procedures. Rotational motion is accomplished by rigidly rotating a subdomain representing the moving component. At the subdomain interface boundary, the faces along the interfaces are extruded into the adjacent subdomain to create new volume elements and provide a one-cell overlap. These new volume elements close the control volumes for the nodes on the interface surface and allow a flux to be computed across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are found by interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. A parallel implementation of the neighbor search is used to find the extruded points in the adjacent subdomain. The method has been implemented in a parallel, node-centered finite volume, high-resolution viscous flow solver. The method does not impose any restrictions on the subdomain interface aside from the axisymmetric limitation required for rotational motion. In addition, the grid on the subdomain interface is arbitrary. The boundary surfaces between the two subdomains can have independent grids from one another. They do not have to connect in a one-to-one manner and there are no symmetry or pattern restrictions placed on the surface grid. A variety of numerical simulations were performed on several small-scale model problems to examine conservation of the interface flux. Overall flux conservation errors were found to be comparable to that for fully connected and fully conservative simulations. In addition, excellent agreement was obtained with both theoretical and experimental results. Three large-scale applications were also used to validate the method and highlight some of the advantages of the sliding interface method compared to the current state-of- the-art for unstructured grid applications. This sliding interface method requires no geometric modifications and has significantly shorter run times Furthermore, there were no apparent adverse effects on the numerical solutions by not strictly enforcing flux conservation at the subdomain boundary.

No description available.

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited fro geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In two-dimensions, an initially symmetric NACA-0012 airfoil and a high-lift multi-element airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in additions, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interactions compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented. / Ph. D.

In this thesis, an approach is presented for the generation of grids suitable for the simulation of high Reynolds number viscous flows in complex three-dimensional geometries. The automatic and reliable generation of such grids is today on the biggest bottlenecks in the industrial CFD simulation environment. In the proposed approach, unstructured tetrahedral grids are employed for the regions far from the viscous boundaries of the domain, while semi-structured layers of high aspect ratio prismatic and hexahedral elements are used to provide the necessary grid resolution inside the boundary layers and normal to the viscous walls. The definition of the domain model is based on the STEP ISO standard and the topological information contained in the model is used for applying the hierarchical grid generation parameters defined by the user. An efficient, high-quality and robust algorithm is presented for the generation of the unstructured simplicial (triangular of tetrahedral) part of the grid. The algorithm is based on the Delaunay triangulation and the internal grid points are created following a centroid or frontal approach. For the surface grid generation, a hybrid approach is also proposed similar to the volume. Semi-structured grids are generated on the surface grid (both on the edges and faces of the domain) to improve the grid resolution around convex and concave ridges and corners, by aligning the grid elements in the directions of high solution gradients along the surface. A method is also developed for automatically setting the grid generation parameters related to the surface grid generation based on the curvature of the surface in order to obtain an accurate and smooth surface grid. Finally, a semi-structured prismatic/hexahedral grid generation algorithm is presented for the generation of the part of grid close to the viscous walls of the domain. The algorithm is further extended with improvements meant to increase the grid quality around concave and convex ridges of the domain, where the semi-structured grids are known to be inadequate. The combined methodology is demonstrated on a variety of complex examples mainly from the automotive and aeronautical industry.

De nombreux domaines utilisent à présent de nouveaux types de grilles composées de polyèdres arbitraires, autrement dit des grilles fortement non-structurées. La problématique de cette thèse concerne la définition de nouveaux outils de visualisation et de calcul sur de telles grilles. Pour la visualisation, cela pose à la fois le problème du stockage et de l'adaptativité des algorithmes à une géométrie et une topologie variables. Pour le calcul, cela pose le problème de la résolution de grands systèmes linéaires creux non-structurés. Pour aborder ces problèmes, l'augmentation incessante de la puissance de calcul parallèle des processeurs graphiques nous fournit de nouveaux outils. Toutefois, l'utilisation de ces GPU nécessite de définir de nouveaux algorithmes adaptés aux modèles de programmation parallèle qui leur sont spécifiques. Nos contributions sont les suivantes : (1) Une méthode générique de visualisation tirant partie de la puissance de calcul des GPU pour extraire des isosurfaces à partir de grandes grilles fortement non-structurées. (2) Une méthode de classification de cellules qui permet d'accélérer l'extraction d'isosurfaces grâce à une pré-sélection des seules cellules intersectées. (3) Un algorithme d'interpolation temporelle d'isosurfaces. Celui-ci permet de visualiser de manière continue dans le temps l'évolution d'isosurfaces. (4) Un algorithme massivement parallèle de résolution de grands systèmes linéaires non-structurés creux sur le GPU. L'originalité de celui-ci concerne son adaptation à des matrices de motif arbitraire, ce qui le rend applicable à n'importe quel système creux, dont ceux issus de maillages fortement non-structurés / This thesis proposes new tools for visualization and computation on strongly unstructured grids. Visualization of such grids that have variable geometry and topology, poses the problem of how to store data and how algorithms could handle such variability. Doing computations on such grids poses the problem of solving large sparse unstructured linear systems. The ever-growing parallel power of GPUs makes them more and more valuable for handling theses tasks. However, using GPUs calls for defining new algorithms highly adapted to their specific programming model. Most recent algorithms for Geometry Processing or Computational Fluid Dynamics (CFD) are using new types of grids made of arbitrary polyhedra, in other words strongly unstructured grids. In case of CFD simulations, these grids can be mapped with scalar or vector fields representing physical properties (for example : density, porosity, permeability). Our contributions are: (1) An efficient generic visualization method that uses GPU's power to accelerate isosurface extraction for large unstructured grids. (2) An adaptative cell classification method that accelerates isosurface extraction by pre-selecting only intersected cells. (3) An efficient algorithm for temporal interpolation of isosurfaces. This algrithm helps to visualize in a continuous maner the evolution of isosurfaces through time. (4) A massively parallel algorithm for solving large sparse unstructured linear systems on the GPU. Its originality comes from its adaptation to sparse matrices with random pattern, which enables to solve any sparse linear system, thus the ones that come from strongly unstructured grids

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / In reservoir simulation, the compositional model is one of the most used models for enhanced oil recovery. However, the physical model involves a large number of equations with a very complex interplay between equations. The model is basically composed of balance equations and equilibrium constraints. The way these equations are solved, the degree of implicitness, the selection of the primary equations, primary and secondary variables have a great impact on the computation time. In order to verify these effects, this work proposes the implementation and comparison of some implicit and semi-implicit methods. The following formulations are tested: an IMPEC (implicit pressure, explicit composition), an IMPSAT (implicit pressure and saturations), and two fully implicit formulations, in which one these formulations is being proposed in this work. However, the literature reports some intrinsic inconsistencies of the IMPSAT formulation mentioned. In order to verify it, an iterative IMPSAT is implemented to check the quality of the IMPSAT method previously mentioned. The finite volume method is used to discretize the formulations using Cartesian grids and unstructured grids in conjunction with the EbFVM (Element based finite volume method) for 2D and 3D reservoirs. The implementations have been performed in the UTCOMP simulator from the University of Texas at Austin. The results of several case studies are compared in terms of volumetric oil and gas rates and the total CPU time. It was verified that the FI approaches increase their performance, when compared to the other approaches, as the grid is refined. A good performance was observed for the IMPSAT approach when compared to the IMPEC formulation. However, as more complex stencils are used, the IMPSAT performance reduces. / Em simulaÃÃo de reservatÃrios, o modelo composicional à um dos mais usados para a recuperaÃÃo avanÃada de petrÃleo. Entretanto, o modelo fÃsico envolve um grande nÃmero de equaÃÃes com uma complexa interelaÃÃo entre elas. O modelo à basicamente composto por equaÃÃes de balanÃo e restriÃÃes de equilÃbrio. A forma como essas equaÃÃes sÃo resolvidas como, o grau de implicitude, a seleÃÃo das equaÃÃes primÃrias, variÃveis primÃrias e secundÃrias tem um grande impacto no tempo de computaÃÃo. Com o intuito de verificar esse efeito, esse trabalho propÃe a implementaÃÃo e comparaÃÃo de alguns mÃtodos implÃcitos e semi-implÃcitos. As seguintes formulaÃÃes sÃo testadas: uma IMPEC (implicit pressure, explicit composition), uma IMPSAT (implicit pressure and saturations), e duas formulaÃÃes totalmente implicitas, das quais uma destas està sendo proposta neste trabalho. Entretanto, a literatura relata algumas inconsistÃncias intrÃnsecas da formulaÃÃo IMPSAT mencionada. Para verificar isso, um IMPSAT iterativo foi implementado para verificar a qualidade nos resultados do mÃtodo IMPSAT prÃviamente mencionado. O mÃtodo de volumes finitos à usado para discretizar as formulaÃÃes usando malhas Cartesianas e nÃo-estruturadas em conjunto com o EbFVM (Element based finite volume method) para reservatÃrios 2D e 3D. A implementaÃÃo foi realizada no simulador UTCOMP da Univeristy of Texas at Austin. Os resultados de diversos casos de estudo sÃo comparados em termos das vazÃes volumÃtricas de Ãleo e gÃs e do tempo total de CPU. Verificou-se que as abordagens totalmente implÃcitas melhoram sua performance, quando comparado com os demais mÃtodos, a medidaque a malha à refinada. Um bom desempenho foi observado para as formulaÃÃes IMPSAT quando comparadas com a formulaÃÃo IMPEC. Entretando, com o uso de conexÃes mais complexas entre os blocos da malha, o desempho da formulaÃÃo IMPSAT reduziu.

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.