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Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

Description: We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two- and three-dimensional flow problems.
Date: December 31, 2008
Creator: Persson, P.-O.
Partner: UNT Libraries Government Documents Department

Multi-material incompressible flow simulation using the moment-of-fluid method

Description: The Moment-of-Fluid interface reconstruction technique is implemented in a second order accurate, unstructured finite element variable density incompressible Navier-Stokes solver. For flows with multiple materials, MOF significantly outperforms existing first and second order interface reconstruction techniques. For two material flows, the performance of MOF is similar to other interface reconstruction techniques. For strongly driven bouyant flows, the errors in the flow solution dominate and all the interface reconstruction techniques perform similarly.
Date: January 1, 2009
Creator: Garimella, R V; Schofield, S P; Lowrie, R B; Swartz, B K; Christon, M A & Dyadechko, V
Partner: UNT Libraries Government Documents Department

Reduced order modeling of fluid/structure interaction.

Description: This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.
Date: November 1, 2009
Creator: Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph & Brake, Matthew Robert
Partner: UNT Libraries Government Documents Department

Turbomachinery blade optimization using the Navier-Stokes equations

Description: A method is presented to perform aerodynamic design optimization of turbomachinery blades. The method couples a Navier-Stokes flow solver with a grid generator and numerical optimization algorithm to seek improved designs for transonic turbine blades. A fast and efficient multigrid, finite-volume flow solver provides accurate performance evaluations of potential designs. Design variables consist of smooth perturbations to the blade surface. A unique elliptic-hyperbolic grid generation method is used to regenerate a Navier-Stokes grid after perturbations have been added to the geometry. Designs are sought which improve a design objective while remaining within specified constraints. The method is demonstrated with two transonic turbine blades with different types and numbers of design variables.
Date: December 1, 1997
Creator: Chand, K. K. & Lee, K. 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

Development and application of advanced one-point turbulence models

Description: Full self-preserving solutions in isotropic decay and homogeneous shear flow turbulence have been examined from a basic theoretical standpoint. These constitute solutions for the two-point double and triple velocity correlations that are self-similar at all scales. Consistent with earlier studies, it was found that both isotropic decay and homogeneous shear flow turbulence have full self-preserving solutions. At high Reynolds numbers - with finite viscosity - the full self-preserving solution for isotropic decay corresponds to a t{sup -1} power-law decay whereas that for homogeneous shear flow corresponds to a production-equals-dissipation equilibrium. An alternative derivation of the isotropic results based on group theory considerations was recently achieved by T. Clark and C. Zemach of Los Alamos. These results suggest that such self-preserving solutions are associated with a singularity in the energy spectrum tensor (i.e., the Fourier transform of the two-point double velocity correlation tensor) at zero wave vector. This can have a profound effect on turbulence models. The ultimate goal is to use these two-point results for the development of improved one-point turbulence models for the solution of practical turbulent flows of scientific and engineering interest.
Date: January 1, 1996
Creator: Speziale, C.G.
Partner: UNT Libraries Government Documents Department

Wavy Taylor vortices in plane Couette flow

Description: Path-following techniques applied to a spectral approximation of the solution of the Navier-Stokes Equations have revealed the existence of a new class of solutions to the plane Couette flow problem.
Date: August 1997
Creator: Conley, A. J. & Keller, H. B.
Partner: UNT Libraries Government Documents Department

Time-dependent buoyant puff model for explosive sources

Description: This paper presents a new model for explosive puff rise histories that is derived from the strong conservative form of the partial differential equations of mass, momenta, and total energy that are integrated over space to yield a coupled system of time dependent nonlinear ordinary differential equations (ODEs). By allowing the dimensions of the puff to evolve laterally and horizontally, the initial rising spherical shaped puff evolves into a rising ellipsoidal shaped mushroom cloud. This model treats the turbulence that is generated by the puff itself and the ambient atmospheric turbulence as separate mechanisms in determining the puff history. The puff rise history was found to depend not only upon the mass and initial temperature of the explosion, but also upon the local stability conditions of the ambient atmosphere through which the puff rises. This model was calibrated by comparison with the Roller Coaster experiments, ranging from unstable to very stable atmospheric conditions; the agreement of the model history curves with these experimental curves was within 10%.
Date: October 1, 1997
Creator: Kansa, E.J.
Partner: UNT Libraries Government Documents Department

Numerical and asymptotic studies of complex flow dynamics. Annual report 1993

Description: Using analytical and numerical methods, the investigators have investigated slightly compressible flows modeled by solutions of the Navier-Stokes equations. General analytical results for ODEs and PDEs with highly oscillatory solutions have been obtained. Work has also been completed on the construction of boundary conditions at artificial boundaries for wave propagation problems and for parabolic systems. In the area of dynamical systems, the investigators have analyzed a novel numerical approach to compute branches of invariant tori. A preliminary code has been developed. New results were obtained on the relationship between the true attractor and its numerical approximations for dissipative dynamical systems. An efficient algorithm for the accurate solution of equations with polynomial coefficients has been developed and applications to the solution of the Navier-Stokes equations in disk geometry have begun.
Date: December 31, 1993
Creator: Coutsias, E.; Hagstrom, T. & Lorenz, J.
Partner: UNT Libraries Government Documents Department

Forward-in-Time Differencing for Fluids: Nonhydrostatic Modeling of Rotating Stratified Flow on a Mountainous Sphere

Description: Traditionally, numerical models for simulating planetary scale weather and climate employ the hydrostatic primitive equations-an abbreviated form of Navier-Stokes equations that neglect vertical accelerations and use simplified inertial forces. 1 Although there is no evidence so far that including nonhydrostatic effects in global models has any physical significance for large scale solutions, there is an apparent trend in the community toward restoring Navier-Stokes equations (or at least their less constrained forms) in global models of atmospheres and oceans. The primary motivation for this is that the state-of-the-art computers already admit resolutions where local nonhydrostatic effects become noticeable. Other advantages include: the convenience of local mesh refinement; better overall accuracy; insubstantial computational overhead relative to hydrostatic models; universality and therefore convenience of maintaining a single large code; as well as conceptual simplicity and mathematical elegancy--features important for education. The few existing nonhydrostatic global models differ in analytic formulation and numerical design, reflecting their different purposes and origins. Much of our present research improves the design of a high-performance numerical model for simulating the flows of moist (and precipitating), rotating, stratified fluids past a specified time-dependent irregular lower boundary. This model is representative of a class of nonhydrostatic atmospheric codes employing the an elastic equations of motion in a terrain-following curvilinear framework, and contains parallel implementations of semi-Lagrangian and Eulerian approximations selectable by the user. The model has been employed in a variety of applications; the quality of results suggest that modern nonoscillatory forward-in-time (NFT) methods are superior to the more traditional centered-in-time-and-space schemes, in terms of accuracy, computational efficiency, flexibility and robustness.
Date: March 31, 1999
Creator: Smolarkiewicz, P.K.; Grubisic, V. & Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Two-point correlation equations for variable density turbulence

Description: A complete set of two-point correlation equations for variable-density turbulence is derived to consistent order in mass-weighted variables (Favre averaging). The derivation is based on a two-point generalization of the Reynolds stress tensor. The equations are transformed with respect to the separation between the two points to Fourier space. The correlation equations, as well as the Fourier-transformed equations, provide insights that are unavailable in the one-point equations. The derivation of spectral closures is significantly more complicated than that of constant-density closures or one-point variable-density closures due to the complex nature of isotropic scalar-vector correlation functions for nonsolenoidal fields. Several necessary constraints for the correlation functions are presented. In addition, a simple spectral model that satisfies these constraints is presented for illustrative purposes, and a discussion of the two-point correlations and their relationship to the corresponding correlations arising in one-point derivations is provided.
Date: June 1, 1995
Creator: Clark, T.T. & Spitz, P.B.
Partner: UNT Libraries Government Documents Department

Automatic differentiation and Navier-Stokes.

Description: We describe the use of automatic differentiation (AD) to enhance a compressible Navier-Stokes model. With the solver, AD is used to accelerate convergence by more than an order of magnitude. Outside the solver, AD is used to compute the derivatives needed for optimization. We emphasize the potential for performance gains if the programmer does not treat AD as a black box, but instead utilizes high-level knowledge about the nature of the application.
Date: December 17, 1997
Creator: Bischof, C.; Hovland, P. & Mohammadi, B.
Partner: UNT Libraries Government Documents Department

Drop Dynamics and Speciation in Isolation of Metals from Liquid Wastes by Reactive Scavenging

Description: Computational and experimental studies of the motion and dynamics of liquid drops in gas flows were conducted with relevance to reactive scavenging of metals from atomized liquid waste. Navier-Stoke's computations of deformable drops revealed a range of conditions from which prolate drops are expected, and showed how frajectiones of deformable drops undergoing deceleration can be computed. Experimental work focused on development of emission fluorescence, and scattering diagnostics. The instrument developed was used to image drop shapes, soot, and nonaxisymmetric departures from steady flow in a 22kw combustor
Date: August 30, 2002
Creator: Pearlstein, Arne J. & Scheeline, Alexander
Partner: UNT Libraries Government Documents Department

Large eddy simulation of flow in LWR fuel bundles.

Description: Advances in computational fluid dynamics (CFD), turbulence modeling, and parallel computing have made feasible the development of codes that can simulate 3-D flows and heat transfer in realistic LWR fuel bundle geometries. Although no single existing RANS (Reynolds averaging of the Navier Stokes equations) turbulence model predicts a sufficiently wide range of flows with accuracy adequate for engineering needs, at this time for most flows the k-{epsilon} models seem to be the best choice. In Ref. 1, it was shown that in LWR fuel-bundle flows the predictions of these models for turbulence intensity are in significant disagreement with experimental measurements. The objective of this work was to assess the predictive power of the constant-coefficient Smagorinsky Large Eddy Simulation (LES) model, the simplest of the LES models, in a typical single-phase LWR fuel-bundle flow.
Date: August 17, 2001
Creator: Tzanos, C. P.
Partner: UNT Libraries Government Documents Department

Numerical Simulations of Shock-Induced Mixing and Combustion

Description: In this paper we use numerical simulation to investigate shock-induced ignition and combustion of a hydrocarbon gas. The focus of this paper is on quantifying the effect of fidelity in the chemical kinetics on the overall solution. We model the system using the compressible Navier Stokes equations for a reacting mixture. These equations express conservation of species mass, momentum, total energy.
Date: April 22, 2003
Creator: Bell, J B; Day, M & Kuhl, A L
Partner: UNT Libraries Government Documents Department


Description: A fluid dynamics model for the evolution of salt domes and ridges is presented. The model assumes a rigid substrate, finite thickness of both strata with no slip and a rigid or free surface of overburden. Inertial terms in the Navier-Stokes equations are neglected due to the large viscosities considered and the initial perturbation is taken to be sinusoidal. Finite sine and cosine transforms are used to solve the flow equations and the resulting systems of equations reproduces the velocity field equation of Ramberg's model. Assuming an initial interface, the infinite series solution is truncated to obtain the constants of the integration from the boundary conditions. The interface is then moved to a new position. Thus, the new shape for the interface can be traced for any time. For small perturbations, we obtain results that are approximately those obtained by the linear theory. Results of the numerical solution of the model for both large and small perturbations are presented.
Date: August 1, 1977
Creator: Nasir, N. E. & Dabbousi, O. B.
Partner: UNT Libraries Government Documents Department

Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains

Description: We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
Date: January 13, 2009
Creator: Persson, P.-O.; Bonet, J. & Peraire, J.
Partner: UNT Libraries Government Documents Department

Noise Properties of Rectifying Nanopores

Description: Ion currents through three types of rectifying nanoporous structures are studied and compared for the first time: conically shaped polymer nanopores, glass nanopipettes, and silicon nitride nanopores. Time signals of ion currents are analyzed by power spectrum. We focus on the low-frequency range where the power spectrum magnitude scales with frequency, f, as 1/f. Glass nanopipettes and polymer nanopores exhibit non-equilibrium 1/f noise, thus the normalized power spectrum depends on the voltage polarity and magnitude. In contrast, 1/f noise in rectifying silicon nitride nanopores is of equilibrium character. Various mechanisms underlying the voltage-dependent 1/f noise are explored and discussed, including intrinsic pore wall dynamics, and formation of vortices and non-linear flow patterns in the pore. Experimental data are supported by modeling of ion currents based on the coupled Poisson-Nernst-Planck and Navier Stokes equations. We conclude that the voltage-dependent 1/f noise observed in polymer and glass asymmetric nanopores might result from high and asymmetric electric fields inducing secondary effects in the pore such as enhanced water dissociation.
Date: February 18, 2011
Creator: Powell, M R; Sa, N; Davenport, M; Healy, K; Vlassiouk, I; Letant, S E et al.
Partner: UNT Libraries Government Documents Department

A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids

Description: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
Date: June 1, 2011
Creator: Luo, Hong; Xia, Yidong; Nourgaliev, Robert & Cai, Chunpei
Partner: UNT Libraries Government Documents Department

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

Description: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Date: January 1, 2010
Creator: Luo, Hong; Luo, Luqing; Nourgaliev, Robert & Mousseau, Vincent A.
Partner: UNT Libraries Government Documents Department

Cubic Spline Collocation Method for the Simulation of Turbulent Thermal Convection in Compressible Fluids

Description: A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number, suggesting the existence of ''hard'' turbulence in two-dimensional compressible convection.
Date: January 12, 2005
Creator: Castillo, V M
Partner: UNT Libraries Government Documents Department

A Split-Step Scheme for the Incompressible Navier-Stokes

Description: We describe a split-step finite-difference scheme for solving the incompressible Navier-Stokes equations on composite overlapping grids. The split-step approach decouples the solution of the velocity variables from the solution of the pressure. The scheme is based on the velocity-pressure formulation and uses a method of lines approach so that a variety of implicit or explicit time stepping schemes can be used once the equations have been discretized in space. We have implemented both second-order and fourth-order accurate spatial approximations that can be used with implicit or explicit time stepping methods. We describe how to choose appropriate boundary conditions to make the scheme accurate and stable. A divergence damping term is added to the pressure equation to keep the numerical dilatation small. Several numerical examples are presented.
Date: June 12, 2001
Creator: Henshaw, W & Petersson, N A
Partner: UNT Libraries Government Documents Department

Higher-Order Semi-Implicit Projection Methods

Description: A semi-implicit form of the method of spectral deferred corrections is applied to the solution of the incompressible Navier-Stokes equations. A methodology for constructing semi-implicit projection methods with arbitrarily high order of temporal accuracy in both the velocity and pressure is presented. Three variations of projection methods are discussed which differ in the manner in which the auxiliary velocity and the pressure are calculated. The presentation will make clear that project methods in general need not be viewed as fractional step methods as is often the practice. Two simple numerical examples re used to demonstrate fourth-order accuracy in time for an implementation of each variation of projection method.
Date: September 6, 2001
Creator: Minion, M. L.
Partner: UNT Libraries Government Documents Department