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A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids

Description: A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.
Date: September 23, 2005
Creator: Henshaw, W D
Partner: UNT Libraries Government Documents Department

Overture: An Object-Oriented Framework for Overlapping Grid Applications

Description: The Overture framework is an object-oriented environment for solving partial differential equations on over-lapping grids. We describe some of the tools in Overture that can be used to generate grids and solve partial differential equations (PDEs). Overture contains a collection of C++ classes that can be used to write PDE solvers either at a high level or at a lower level for efficiency. There are also a number of tools provided with Overture that can be used with no programming effort. These tools include capabilities to: repair computer-aided-design (CAD) geometries and build global surface triangulations; generate surface and volume grids with hyperbolic grid generation; generate composite overlapping grids; generate hybrid (unstructured) grids; and solve particular PDEs such as the incompressible and compressible Navier-Stokes equations.
Date: April 4, 2002
Creator: Henshaw, W. D.
Partner: UNT Libraries Government Documents Department

Plotstuff graphics post processor for overture user guide, version 1.00

Description: This document explains how to use plotStuff, a program for plotting results from Overture programs. plotStuff reads data-base files created by Overture that contain information about the grid and solutions, a ''show file''. plotStuff has features for plotting contours, cutting planes, streamlines, iso-surfaces and grids. It can also be used to plot various derived quantities such as derivatives of the solution components. This document describes the class Derived Functions which is used to compute these derived quantities.
Date: April 20, 2000
Creator: Henshaw, W D
Partner: UNT Libraries Government Documents Department

An Algorithm for Projecting Points onto a Patched CAD Model

Description: We are interested in building structured overlapping grids for geometries defined by computer-aided-design (CAD) packages. Geometric information defining the boundary surfaces of a computation domain is often provided in the form of a collection of possibly hundreds of trimmed patches. The first step in building an overlapping volume grid on such a geometry is to build overlapping surface grids. A surface grid is typically built using hyperbolic grid generation; starting from a curve on the surface, a grid is grown by marching over the surface. A given hyperbolic grid will typically cover many of the underlying CAD surface patches. The fundamental operation needed for building surface grids is that of projecting a point in space onto the closest point on the CAD surface. We describe an fast algorithm for performing this projection, it will make use of a fairly coarse global triangulation of the CAD geometry. We describe how to build this global triangulation by first determining the connectivity of the CAD surface patches. This step is necessary since it often the case that the CAD description will contain no information specifying how a given patch connects to other neighboring patches. Determining the connectivity is difficult since the surface patches may contain mistakes such as gaps or overlaps between neighboring patches.
Date: May 29, 2001
Creator: Henshaw, W D
Partner: UNT Libraries Government Documents Department

Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow

Description: We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach.
Date: August 30, 2005
Creator: Henshaw, W D & Schwendeman, D W
Partner: UNT Libraries Government Documents Department

Time-Accurate Computation of Viscous Flow Around Deforming Bodies Using Overset Grids

Description: Dynamically evolving boundaries and deforming bodies interacting with a flow are commonly encountered in fluid dynamics. However, the numerical simulation of flows with dynamic boundaries is difficult with current methods. We propose a new method for studying such problems. The key idea is to use the overset grid method with a thin, body-fitted grid near the deforming boundary, while using fixed Cartesian grids to cover most of the computational domain. Our approach combines the strengths of earlier moving overset grid methods for rigid body motion, and unstructured grid methods for Aow-structure interactions. Large scale deformation of the flow boundaries can be handled without a global regridding, and in a computationally efficient way. In terms of computational cost, even a full overset grid regridding is significantly cheaper than a full regridding of an unstructured grid for the same domain, especially in three dimensions. Numerical studies are used to verify accuracy and convergence of our flow solver. As a computational example, we consider two-dimensional incompressible flow past a flexible filament with prescribed dynamics.
Date: April 2, 2001
Creator: Fast, P & Henshaw, W D
Partner: UNT Libraries Government Documents Department

On cylindrically converging shock waves shaped by obstacles

Description: Motivated by recent experiments, numerical simulations were performed of cylindrically converging shock waves. The converging shocks impinged upon a set of zero to sixteen regularly space obstacles. For more than two obstacles the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. The maximum pressure and temperature as a function of number of obstacles were studied. The self-similar behavior of cylindrical, triangular and square-shaped shocks were also investigated.
Date: July 16, 2007
Creator: Eliasson, V; Henshaw, W D & Appelo, D
Partner: UNT Libraries Government Documents Department

A Study of Detonation Diffraction in the Ignition-and-Growth Model

Description: Heterogeneous high-energy explosives are morphologically, mechanically and chemically complex. As such, their ab-initio modeling, in which well-characterized phenomena at the scale of the microstructure lead to a rationally homogenized description at the scale of observation, is a subject of active research but not yet a reality. An alternative approach is to construct phenomenological models, in which forms of constitutive behavior are postulated with an eye on the perceived picture of the micro-scale phenomena, and which are strongly linked to experimental calibration. Most prominent among these is the ignition-and-growth model conceived by Lee and Tarver. The model treats the explosive as a homogeneous mixture of two distinct constituents, the unreacted explosive and the products of reaction. To each constituent is assigned an equation of state, and a single reaction-rate law is prescribed for the conversion of the explosive to products. It is assumed that the two constituents are always in pressure and temperature equilibrium. The purpose of this paper is to investigate in detail the behavior of the model in situations where a detonation turns a corner and undergoes diffraction. A set of parameters appropriate for the explosive LX-17 is selected. The model is first examined analytically for steady, planar, 1-D solutions and the reaction-zone structure of Chapman-Jouguet detonations is determined. A computational study of two classes of problems is then undertaken. The first class corresponds to planar, 1-D initiation by an impact, and the second to corner turning and diffraction in planar and axisymmetric geometries. The 1-D initiation, although interesting in its own right, is utilized here as a means for interpretation of the 2-D results. It is found that there are two generic ways in which 1-D detonations are initiated in the model, and that these scenarios play a part in the post-diffraction evolution as well. For the parameter ...
Date: April 14, 2006
Creator: Kapila, A K; Schwendeman, D W; Bdzil, J B & Henshaw, W D
Partner: UNT Libraries Government Documents Department

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

Description: A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.
Date: February 13, 2006
Creator: Banks, J W; Schwendeman, D W; Kapila, A K & Henshaw, W D
Partner: UNT Libraries Government Documents Department

CgWind: A high-order accurate simulation tool for wind turbines and wind farms

Description: CgWind is a high-fidelity large eddy simulation (LES) tool designed to meet the modeling needs of wind turbine and wind park engineers. This tool combines several advanced computational technologies in order to model accurately the complex and dynamic nature of wind energy applications. The composite grid approach provides high-quality structured grids for the efficient implementation of high-order accurate discretizations of the incompressible Navier-Stokes equations. Composite grids also provide a natural mechanism for modeling bodies in relative motion and complex geometry. Advanced algorithms such as matrix-free multigrid, compact discretizations and approximate factorization will allow CgWind to perform highly resolved calculations efficiently on a wide class of computing resources. Also in development are nonlinear LES subgrid-scale models required to simulate the many interacting scales present in large wind turbine applications. This paper outlines our approach, the current status of CgWind and future development plans.
Date: February 22, 2010
Creator: Chand, K K; Henshaw, W D; Lundquist, K A & Singer, M A
Partner: UNT Libraries Government Documents Department

Overture: An advanced object-oriented software system for moving overlapping grid computations

Description: While the development of high-level, easy-to-use, software libraries for numerical computations has been successful in some areas (e.g. linear system solvers, ODE solvers, grid generation), this has been an elusive goal for developers of partial differential equation (PDE) solvers. The advent of new high level languages such as C++ has begun to make this an achievable goal. This report discusses an object- oriented environment that we are developing for solving problems on overlapping (Chimera) grids. The goal of this effort is to support flexible PDE solvers on adaptive, moving, overlapping grids that cover a domain and overlap where they meet. Solutions values at the overlap are determined by interpolation. The overlapping grid approach is particularly efficient for rapidly generating high- quality grids for moving geometries since as the component grids move, only the list of interpolation points changes, and the component grids do not have to be regenerated. We use structured component grids so that efficient, fast finite-difference algorithms can be used. Oliger-Berger-Corella type mesh refinement is used to efficiently resolve fine features of the flow.
Date: September 1, 1996
Creator: Brown, D.L. & Henshaw, W.D.
Partner: UNT Libraries Government Documents Department

A primer for writing overlapping grid codes in C++

Description: We describe how to write C++ programs to solve partial differential equations on overlapping grids. We use the grid construction program {bold Ogen} to create overlapping grids. We use the parallel array class library A++ to write efficient and portable serial or parallel code.
Date: October 16, 1996
Creator: Henshaw, W.D.
Partner: UNT Libraries Government Documents Department

Overture: an objectoriented framework for solving partial differential equations on overlapping grids

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It merges geometry, grid generation, difference operators, boundary conditions, data-base access and graphics into an easy to use high level interface.
Date: September 22, 1998
Creator: Brown, D L; Henshaw, W D & Quinlan , D J
Partner: UNT Libraries Government Documents Department

Solution adaptive methods for low-speed and all-speed flows

Description: The goal of this work was to design new fast algorithms that could be used to solve fluid flows at all speeds by building upon the best approaches now available for solving very low speed flows and high speed flows. Furthermore the algorithms developed must be appropriate for use on complex moving geometries and for use with adaptive mesh refinement. The algorithms must also be extendible to chemically reacting (combustion) flows. To this end they have developed new methods for efficiently computing fluid problems that involve low-speed flows and problems that are a mixture of low-speed and high-speed flows. The algorithms have been implemented in 2D and 3D on moving overlapping grids and will be a fundamental component of the chemically reacting flow solvers that they are now developing for industrial applications.
Date: January 1, 1998
Creator: Henshaw, W.D.; Pao, K.I. & Saltzman, J.S.
Partner: UNT Libraries Government Documents Department

Overture: object-oriented tools for overset grid applications

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, data-base access and graphics. Short sample code segments are presented to show the power of this approach.
Date: April 28, 1999
Creator: Brown, D L; Henshaw, W D & Quinlan, D J
Partner: UNT Libraries Government Documents Department

Generating Composite Overlapping Grids on CAD Geometries

Description: We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework.
Date: February 7, 2002
Creator: Henshaw, W.D.
Partner: UNT Libraries Government Documents Department

Overture: an object-oriented software system for solving partial differential equations in serial and parallel environments

Description: The OVERTURE Framework is an object-oriented environment for solving PDEs on serial and parallel architectures. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures, as well as the details of the parallel implementation. It is based on the A++/P++ array class library and is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement and the composite overlapping grid method to represent problems with complex moving geometry.
Date: April 1, 1997
Creator: Brown, D.L.; Chesshire, G.S.; Henshaw, W.D. & Quinlan, D.J.
Partner: UNT Libraries Government Documents Department

Adaptive composite overlapping mesh algorithms on message passing architectures

Description: This project developed high-level computational tools that facilitate the development of fluid flow simulation software using the adaptive composite overlapping mesh method. An objective-oriented approach was take which used the C++ programming language to develop libraries containing C++ classes that provide abstractions of the basic operations required to assemble the required simulation software. Through this approach, it was also possible to hide many of the details of the computations required on parallel computer architectures. Result is the basis for a high-level programming environment that facilitates the development of high-resolution simulation software on serial or parallel computer architectures for the equations describing fluid flow in regions with complex geometry.
Date: August 1997
Creator: Brown, D. L.; Quinlan, D. J.; Chesshire, G. S.; Henshaw, W. D. & Berndt, M.
Partner: UNT Libraries Government Documents Department