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A discontinuous Galerkin front tracking method for two-phase flows with surface tension

Description: A Discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy. Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension.
Date: December 28, 2008
Creator: Nguyen, V.-T.; Peraire, J.; Cheong, K.B. & Persson, P.-O.
Partner: UNT Libraries Government Documents Department

Adjoint Error Estimation for Linear Advection

Description: An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Date: March 30, 2011
Creator: Connors, J M; Banks, J W; Hittinger, J A & Woodward, C S
Partner: UNT Libraries Government Documents Department

High accuracy capture of curved shock fronts using the method of space-time conservation element and solution elemen

Description: Split numerical methods have been commonly used in computational physics for many years due to their speed, simplicity, and the accessibility of shock capturing methods in one-dimension. For a variety of reasons, it has been challenging to determine just how accurate operator split methods are, especially in the presence of curved wave features. One of these difficulties has been the lack of multidimensional shock capturing methods. Another is the difficulty of mathematical analysis of dis-continuous flow phenomena. Also, computational studies have been limited due to a lack of multidimensional model problems with analytic solutions that probe the nonlinear features of the flow equations. However, a new genuinely unsplit numerical method has been invented. With the advent of the Space-Time Conservation Element/Solution Element (CE/SE) method, it has become possible to attain high accuracy in multidimensional flows, even in the presence of curved shocks. Examples presented here provide some new evidence of the errors committed in the use of operator split techniques, even those employing ´┐Żunsplit´┐Ż corrections. In these problems, the CE/SE method is able to maintain the original cylindrical symmetry of the problem and track the main features of the flow, while the operator split methods fail to maintain symmetry and position the shocks incorrectly, particularly near the focal point of the incomi
Date: October 23, 1998
Creator: Cook, Jr., G
Partner: UNT Libraries Government Documents Department

Multidimensional Conservation Laws and Low Regularity Solutions

Description: This is the concluding report for the project, a continuation of research by Keyfitz and co-workers on multidimensional conservation laws, and applications of nonhyperbolic conservation laws in the two-fluid model for multiphase flow. The multidimensional research project was started with Suncica Canic, at the University of Houston and with Eun Heui Kim, now at California State University Long Beach. Two postdoctoral researchers, Katarina Jegdic and Allen Tesdall, also worked on this research. Jegdic's research was supported (for a total of one year) by this grant. Work on nonhyperbolic models for two-phase flows is being pursued jointly with Michael Sever, Hebrew University. Background for the project is contained in earlier reports. Note that in 2006, the project received a one-year no-cost extension that will end in September, 2007. A new proposal, for continuation of the research and for new projects, will be submitted in the Fall of 2007, with funding requested to begin in the summer of 2008. The reason for the 'funding gap' is Keyfitz's four-year stint as Director of the Fields Institute in Toronto, Canada. The research has continued, but has been supported by Canadian grant funds, as seems appropriate during this period.
Date: June 16, 2007
Creator: Keyfitz, Barbara Lee
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

Few group collapsing of covariance matrix data based on a conservation principle

Description: A new algorithm for a rigorous collapsing of covariance data is proposed, derived, implemented, and tested. The method is based on a conservation principle that allows preserving at a broad energy group structure the uncertainty calculated in a fine group energy structure for a specific integral parameter, using as weights the associated sensitivity coefficients.
Date: June 24, 2008
Creator: Hiruta,H.; Palmiotti, G.; Salvatores, M.; Arcilla, Jr., R.; Oblozinsky, P. & McKnight, R.D.
Partner: UNT Libraries Government Documents Department

A Cartesian embedded boundary method for hyperbolic conservation laws

Description: The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Date: December 4, 2006
Creator: Sjogreen, B & Petersson, N A
Partner: UNT Libraries Government Documents Department

Two-Phase Model of Combustion in Explosions

Description: A two-phase model for Aluminum particle combustion in explosions is proposed. It combines the gas-dynamic conservation laws for the gas phase with the continuum mechanics laws of multi-phase media, as formulated by Nigmatulin. Inter-phase mass, momentum and energy exchange are prescribed by the Khasainov model. Combustion is specified as material transformations in the Le Chatelier diagram which depicts the locus of thermodynamic states in the internal energy-temperature plane according to Kuhl. Numerical simulations are used to show the evolution of two-phase combustion fields generated by the explosive dissemination of a powdered Al fuel.
Date: June 19, 2006
Creator: Kuhl, A L; Khasainov, B & Bell, J
Partner: UNT Libraries Government Documents Department

A Freestream-Preserving High-Order Finite-Volume Method for Mapped Grids with Adaptive-Mesh Refinement

Description: A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). Advancement in time is achieved with a fourth-order Runge-Kutta method.
Date: December 16, 2011
Creator: Guzik, S; McCorquodale, P & Colella, P
Partner: UNT Libraries Government Documents Department

CPT and superstring

Description: The authors discuss the possibility that CPT violation may appear as a consequence of microscopic decoherence due to quantum-gravity effects, that they describe using a density-matrix formalism motivated by their studies of non-critical string theory. The maximum possible order of magnitude of such decohering CPT-violating effects is not far from the sensitivity of present experiments on the neutral kaon system, and they review a simple parametrization for them. The authors also review a recent data analysis carried out together with the CPLEAR collaboration, which bounds any such decohering CPT-violating parameters to be {approx_lt} 10{sup {minus}19} GeV.
Date: July 1, 1996
Creator: Ellis, J.; Mavromatos, N.E. & Nanopoulos, D.V.
Partner: UNT Libraries Government Documents Department

Multiphase saturation equations, change of type and inaccessible regions

Description: We identify a class of flux functions which give rise to conservation laws which are hyperbolic except along a codimension one subspace of state space. We show that a number of systems modeling porous medium flow can be regarded as perturbations of such systems, and describe the phenomenon of change of type for these perturbations. We also discuss a property of solutions of such systems, the existence of inaccessible regions - subsets of state space which appear to be avoided by solutions.
Date: December 31, 1992
Creator: Keyfitz, B.L.
Partner: UNT Libraries Government Documents Department

Shock stability in systems that change type. Final grant report to the Department of Energy

Description: The aim of the original project was to investigate systems of conservation laws that change type. Progress was made on this problem. During the last period of the grant, the author began an investigation of a multidimensional system related to Mach reflection which goes beyond the original work proposed. This has been fruitful direction in which to apply expertise on change of type. Some basic theoretical results have been found.
Date: November 10, 1995
Creator: Keyfitz, B.L.
Partner: UNT Libraries Government Documents Department

Two-Phase Potential Flow. Final report

Description: The objective of this work was to devise essentially exact solutions to a set of well-defined basic problems of inviscid fluid flow with particulate inclusions. This would help to establish a sound basis for fundamental theoretical developments in the field of two-phase flow. The results of this effort have ranged from basic theorems and the formulation of conservation laws for two-phase mixtures, to detailed predictions for specific geometrical patterns and experimental confirmation of these results.
Date: June 11, 1999
Creator: Wallis, G.B.
Partner: UNT Libraries Government Documents Department

Dispersive Approximations for Hyperbolic Conservation Laws

Description: Necessary and sufficient conditions are given so that the Sobolev-type partial differential equations generate a contraction semigroup. It is shown that any nonlinear contraction from L/sup 1/(R) to itself that preserves the integral and commutes with translations satisfies maximum and minimum principles. This lemma is applied to the solution operator S/sub t/ to give necessary and sufficient conditions that S/t/ satisfy a maximum principle, despite the dispersive nature. Sufficient conditions are given so that the solutions converge, as nu and beta tend to zero, to the entropy solution of the conservation law. A larger class of monotone finite-difference schemes for the numerical solution of the conservation law motivated by finite-difference discretizations of the Sobolev equations, is introduced, and convergence results are proved for methods in this class. The methods analyzed include some that were previously used to approximate the solution of a linear waterflood problem in petroleum engineering.
Date: December 1981
Creator: Lucier, Bradley J.
Partner: UNT Libraries Government Documents Department

Energy changes in transforming solids annual report, February 1, 1994--January 31, 1995

Description: The recently formulated thermodynamic theory of elastic bodies prone to damage has been further developed. This formalism is based on classical thermodynamics using the local state approximation, with a significant amount of attention paid to non-isothermal processes. Certain concepts are being clarified via the use of Onsager`s reciprocal relations. Planned work includes a significant effort to develop the fundamental elements of an exact thermodynamic theory, which until now has been restricted to the one-dimensional case, and will be extended to two and three dimensions. Information is also included on publications in print, in press, and submitted since the last report (8/92).
Date: July 1, 1993
Creator: Herrmann, G. & Barnett, D.M.
Partner: UNT Libraries Government Documents Department

Computer simulation of FCC riser reactors.

Description: A three-dimensional computational fluid dynamics (CFD) code, ICRKFLO, was developed to simulate the multiphase reacting flow system in a fluid catalytic cracking (FCC) riser reactor. The code solve flow properties based on fundamental conservation laws of mass, momentum, and energy for gas, liquid, and solid phases. Useful phenomenological models were developed to represent the controlling FCC processes, including droplet dispersion and evaporation, particle-solid interactions, and interfacial heat transfer between gas, droplets, and particles. Techniques were also developed to facilitate numerical calculations. These techniques include a hybrid flow-kinetic treatment to include detailed kinetic calculations, a time-integral approach to overcome numerical stiffness problems of chemical reactions, and a sectional coupling and blocked-cell technique for handling complex geometry. The copyrighted ICRKFLO software has been validated with experimental data from pilot- and commercial-scale FCC units. The code can be used to evaluate the impacts of design and operating conditions on the production of gasoline and other oil products.
Date: April 20, 1999
Creator: Chang, S. L.; Golchert, B.; Lottes, S. A.; Petrick, M. & Zhou, C. Q.
Partner: UNT Libraries Government Documents Department

A cartesian grid embedded boundary method for hyperbolic conservation laws

Description: We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
Date: October 3, 2004
Creator: Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J. & Modiano, David
Partner: UNT Libraries Government Documents Department


Description: Recent progress in the field of noninterferometric phase retrieval brings the ordinary Fresnel microscopy to a new quantitative level, suitable for recovering both the amplitude and phase of the object, based on image intensity measurements of the object. We show that this is sufficient for in-plane component mapping of magnetic induction for small magnetic elements with known geometry ranging from micro- to few nanometers size. In present paper we re-examine some conservation principles used for the transport-of-intensity (TIE) equation derived by Teaque for application to phase retrieval in light and X-ray optics. In particular, we prove that the intensity conservation law should be replaced in general case with the energy-flow conservation law. This law describes the amplitude-phase balance of the partially coherent beam on its propagation along the optical path, valid both for light and electron optics. This substitution has at least two important fundamental consequences.
Date: August 4, 2002
Creator: VOLKOV,V.V. & ZHU,Y.
Partner: UNT Libraries Government Documents Department

Multi-Fluid Model of Exothermic Fields in Explosions

Description: A Multi-fluid Model is proposed for turbulent combustion in explosions at infinitely-large Reynolds, Peclet & Damkoehler numbers. It is based on the gas dynamic conservation laws for the mixture, augmented mass-energy conservation laws for each fluid (fuel-F, oxidizer-A and products-P). Combustion is treated as material transformations in the Le Chatelier plane--rather than ''heat release'' found in traditional models. This allows one to construct thermodynamically-consistent representations of the fluids. Such transformations occur at an exothermic front--which represents, simultaneously, a sink for F & A and source of P. The front is represented by a Dirac delta function at the stoichiometric contour in the turbulent field. This Model then provides an extraordinarily clear picture of turbulent combustion fields, which are normally clouded by a myriad of diffusional effects.
Date: February 5, 2000
Creator: Kuhl, A.L.; Oppenheim, A.K. & Ferguson, R.E.
Partner: UNT Libraries Government Documents Department

Solving partial differential equations on irregular domains with moving interfaces, with applications to superconformal electrodeposition in semiconductor manufacturing

Description: We present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces. Instead of the typical approach of solving in a larger rectangular domain, our approach performs most calculations only in the desired domain. To do so efficiently, we have developed a one-sided multigrid method to solve the corresponding large sparse linear systems. Our focus is on the simulation of the electrodeposition process in semiconductor manufacturing in both two and three dimensions. Our goal is to track the position of the interface between the metal and the electrolyte as the features are filled and to determine which initial configurations and physical parameters lead to superfilling. We begin by motivating the set of equations which model the electrodeposition process. Building on existing models for superconformal electrodeposition, we develop a model which naturally arises from a conservation law form of surface additive evolution. We then introduce several numerical algorithms, including a conservative material transport level set method and our multigrid method for one-sided diffusion equations. We then analyze the accuracy of our numerical methods. Finally, we compare our result with experiment over a wide range of physical parameters.
Date: December 10, 2007
Creator: Sethian, J.A. & Shan, Y.
Partner: UNT Libraries Government Documents Department

An assessment of semi-discrete central schemes for hyperbolic conservation laws.

Description: High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume ...
Date: September 1, 2003
Creator: Christon, Mark Allen; Robinson, Allen Conrad & Ketcheson, David Isaac
Partner: UNT Libraries Government Documents Department

Numerical Simulations of Thermobaric Explosions

Description: A Model of the energy evolution in thermobaric explosions is presented. It is based on the two-phase formulation: conservation laws for the gas and particle phases along with inter-phase interaction terms. It incorporates a Combustion Model based on the mass conservation laws for fuel, air and products; source/sink terms are treated in the fast-chemistry limit appropriate for such gas dynamic fields. The Model takes into account both the afterburning of the detonation products of the booster with air, and the combustion of the fuel (Al or TNT detonation products) with air. Numerical simulations were performed for 1.5-g thermobaric explosions in five different chambers (volumes ranging from 6.6 to 40 liters and length-to-diameter ratios from 1 to 12.5). Computed pressure waveforms were very similar to measured waveforms in all cases - thereby proving that the Model correctly predicts the energy evolution in such explosions. The computed global fuel consumption {mu}(t) behaved as an exponential life function. Its derivative {dot {mu}}(t) represents the global rate of fuel consumption. It depends on the rate of turbulent mixing which controls the rate of energy release in thermobaric explosions.
Date: May 4, 2007
Creator: Kuhl, A L; Bell, J B; Beckner, V E & Khasainov, B
Partner: UNT Libraries Government Documents Department

Dense Heterogeneous Continuum Model of Two-Phase Explosion Fields

Description: A heterogeneous continuum model is proposed to describe the dispersion of a dense Aluminum particle cloud in an explosion. Let {alpha}{sub 1} denote the volume fraction occupied by the gas and {alpha}{sub 2} the fraction occupied by the solid, satisfying the volume conservation relation: {alpha}{sub 1} + {alpha}{sub 2} = 1. When the particle phase occupies a non-negligible volume fraction (i.e., {alpha}{sub 2} > 0), additional terms, proportional to {alpha}{sub 2}, appear in the conservation laws for two-phase flows. These include: (i) a particle pressure (due to particle collisions), (ii) a corresponding sound speed (which produces real eigenvalues for the particle phase system), (iii) an Archimedes force induced on the particle phase (by the gas pressure gradient), and (iv) multi-particle drag effects (which enhance the momentum coupling between phases). These effects modify the accelerations and energy distributions in the phases; we call this the Dense Heterogeneous Continuum Model. A characteristics analysis of the Model equations indicates that the system is hyperbolic with real eigenvalues for the gas phase: {l_brace}v{sub 1}, v{sub 1} {+-} {alpha}{sub 1}{r_brace} and for the 'particle gas' phase: {l_brace}v{sub 2}, v{sub 2} {+-}{alpha}{sub 2}{r_brace} and the particles: {l_brace}v{sub 2}{r_brace}, where v{sub i} and {alpha}{sub i} denote the velocity vector and sound speed of phase i. These can be used to construct a high-order Godunov scheme to integrate the conservation laws of a dense heterogeneous continuum.
Date: April 7, 2010
Creator: Kuhl, A L & Bell, J B
Partner: UNT Libraries Government Documents Department