Adaptive Meshing for Discontinuous Galerkin Finite Elements
R. B. Haber*, H. Edelsbrunner* (Duke Univ.), D. R. Grayson* (Mathematics), S. Teng* (Comput. Sci.), J. M. Sullivan* (Mathematics), C. Heeren, A. Sheffer, A. Ungor
NSF/DARPA Center for Process Simulation and Design; DOE Center for Simulation of Advanced Rockets

This project supports numerical research in both the Center for Process Simulation and Design and the Center for Simulation of Advanced Rockets. The objective is to develop algorithms for mesh generation and adaptive refinement that are responsive to the special requirements of discontinuous Galerkin (DG) finite element methods as applied to problems with moving boundaries and evolving topologies. Specific topics include mesh-generation algorithms for four-dimensional space-time grids, an object-oriented geometry library for adaptive DG methods, a new theorem for edge-wise subdivision of n-simplices, and new algorithms for adapting hexahedral grids to evolving geometry.

Center for Process Simulation and Design
R. B. Haber,* J. A. Dantzig (Mech. & Indus. Engr.),H. Edelsbrunner (Duke Univ.), D. R. Grayson (Mathematics), M. T. Heath (Comput. Sci.), R. L. Jerrard (Mathematics), L. Kale (Comput. Sci.), D. A. Padua* (Comput. Sci.), S. Teng (Comput. Sci.), J. M. Sullivan* (Mathematics), D. A. Tortorelli (Mech. & Indus. Engr.)
National Science Foundation, DMS 98-73945; Defense Advanced Research Projects Agency

This research initiative establishes new collaborations among mathematicians, engineers, and computer scientists to enable multiscale simulations of the complex, nonlinear behavior that underlies process and product design. Specifically, the investigators model microstructural development associated with dentritic growth in casting processes and with the evolution of texture and grain-boundary precipitates in extrusion and quench processes. Methods include anisotropic error estimates that drive 'smart' mesh generators and adaptive finite-element procedures, gridless level-set methods, space-time finite-element models, parallel solution techniques, and nonlinear programming strategies. JAVA-based programming environments as well as compile-time and run-time code optimizers are used to produce portable, high-performance parallel codes.

Combustion-driven Fracture and Debonding
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.), L. Yin
DOE Center for Simulation of Advanced Rockets

Our focus is on mesoscale (i.e., pertaining to length scales associated with the propellant grain structure) simulations of fracture and debonding in solid-fuel engines. Simulations will be based on cohesive fracture models implemented in a space-time discontinuous Galerkin finite-element code. Large-scale, parallel computing methods will be developed to enable three-dimensional fracture simulations. Existing cohesive failure models will be extended to model viscoelastic fracture and debonding processes observed in solid-fuel engines. The long-term objective is to simulate crack growth and debonding driven by an active combustion process.

Direct Numerical Simulation of 2-D Cellular Detonation Waves
M. Short*
U.S. Air Force Office of Scientific Research, F49620-96-1-0260

Using modern finite-volume techniques and adaptive mesh refinement methods, we seek to simulate the formation of cellular detonations in very wide rectangular channels. Several different finite-volume methods are being investigated to determine those that best overcome the many numerical irregularities associated with the computation of high-speed flow. We are also seeking efficient methods for including complex chemical reactions in the detonation flow.

Motion of Propellant Combustion Interface
D. S. Stewart*
DOE Center for Simulation of Advanced Rockets

A model for the motion of the propellant combustion interface inside a solid rocket motor is being developed. The initial model will be based on the propagation of a normal surface; hence the combustion layer will be modeled as a surface of discontinuity. Different surface representations that employ level sets are being considered.

Parallel Implementations of Discontinuous Galerkin Finite-Element Methods
R. B. Haber,* M. T. Heath* (Comput. Sci.), L. Kale* (Comput. Sci.), D. A. Padua* (Comput. Sci.), N. Sobh, D. A. Tortorelli* (Mech. & Indus. Engr.)
NSF/DARPA Center for Process Simulation and Design; DOE Center for Simulation of Advanced Rockets

This project supports numerical research in both the Center for Process Simulation and Design and the Center for Simulation of Advanced Rockets. The objective is to develop parallel algorithms for discontinuous Galerkin (DG) finite-element methods for hyperbolic, parabolic and elliptic boundary-value problems. Both a shared-memory technique and an adaptive distributed-memory algorithm using data-driven objects are under investigation. Excellent speed-ups have been obtained for element-by-element solutions of DG approximations to hyperbolic problems. We are also investigating new preconditioners for iterative solvers that exploit the special structure of DG methods.

Phase-Field Elasticity as Applied to Phase Transitions and Fracture
E. Fried,* M. E. Gurtin (Carnegie Mellon Univ.)
U.S. Department of Energy, 96-DOE-F-1682

This project focuses on the development of phase-field models that regularize conventional theories for solid-state phase transitions and dynamical fracture along with associated numerical methods. The goal is to apply these models to study nucleation and the development of fine structure during phase transitions and also to the initiation, branching, splitting, crossing, and coalescence of cracks during dynamical fracture processes.

Process Modeling and Otimization for Crashworthiness of Extruded Aluminum Components
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.), N. Sobh, J. Huang, C. Wang, L. Yin, R. W. Hyland, Jr. (Alcoa), L. Lalli (Alcoa), P. Wang (Alcoa)
National Science Foundation, DMI-9700460; Alcoa Corp.

The objective of this project is to improve the crashworthiness of extruded aluminum automotive components by simultaneously optimizing process and product designs. Researchers at the University of Illinois are developing macroscopic simulations of extrusion and quench processes with embedded microstructure evolution models. These predict precipitate evolution, crystallographic texture, and residual stress. Discontinuous Galerkin finite-element models accommodate large-scale microstructure models with thousands of degrees of freedom per material point. Nonlinear programming methods optimize process parameters and tool geometry to achieve improved performance.

Program-Burn and Level-Set Technology
D. S. Stewart,* J. Bdzil (LANL)
Los Alamos National Laboratory, DOE/LANL I2933-0019

We approximate detonation flows with finite-length reaction zones behind a shock with a single discontinuous front. The numerical algorithm called Program Burn (PB) captures end states that are consistent with those found from the theory of detonation shock dynamics (the asymptotic theory for weak detonation shock curvature). Exact solutions of the reactive Euler equations are compared with the PB model and excellent comparisons are found.

Pulsed Detonation Engines
M. Short*
U.S. Air Force Office of Scientific Research, AF MS 1313 Antic

Pulsed detonation engines (PDE) are a novel type of propulsion mechanism for hypersonic flight. Their operating principle relies on (1) igniting a detonation at one end of a tube (engine) generating thrust; (2) allowing the detonation to pass out of the tube; (3) evacuating the exhaust material; (4) refilling the engine with fuel and reigniting the detonation (all at a rate of 100 Hz). Currently we are simulating this complex process numerically in order to develop simplified models of the PDE operation.

Simulation of Mantle Convection
S. Balachandar,* D. A. Yuen*
National Science Foundation, DMS 96-22889; Minnesota Supercomputer Institute; U.S. Army High-Performance Computing and Research Center

The strongly chaotic convective flow in the Earth's mantle is well evident through its surface manifestations of mountain formation, continental break-up, and volcanic activity. Here we model mantle convection with an anelastic-liquid approximation, which accounts for depth-dependent thermodynamic and transport properties. Internal heat generation and multiple phase transitions are included in this formalism. The resulting complex variable-coefficient PDEs are solved efficiently using spectral-method techniques. Massively parallel computing and large-scale graphics are an integral part of this ongoing program.

Simulation of Turbulent Mixing in Stirred-Tank Reactors
S. Balachandar,* R. J. Adrian,* K. Kar, H. S. Yoon
Dow Chemical Co.

Stirred-tank reactors are commonly used in the chemical industry for mixing and chemical reaction. Their design and scale-up process typically relies heavily on a series of expensive laboratory-scale experiments and pilot plants. On the other hand, the predictive capability of conventional Reynolds-averaged Navier-Stokes simulations has been observed by the industry to be less than adequate in accurately accounting for the large-scale dynamics and their effect on stirring and mixing. This project seeks to develop a novel predictive methodology that combines the power of large-eddy simulation and particle-image velocimetry.

Space-Time Finite Elements for Solid-Combustion-Fluid Interaction in Solid-Fuel Rocket Engines
R. B. Haber,* R. D. Moser,* D. A. Tortorelli* (Mech. & Indus. Engr.), N. Sobh, A. Acharaya, J. Palaniappan, L. Yin
DOE Center for Simulation of Advanced Rockets

This project addresses the problem of interfacing solid mechanics simulations of propellant and casing structures with simulations of combustion and turbulent flow. Space-time discontinuous Galerkin (DG) finite-element models are under development to represent time-varying material domains (e.g., due to combustion) and to support time-dependent mesh adaptation. A new element-by-element DG method for elastodynamics, with breakthrough efficiency and local conservation properties, has been demonstrated. Proper treatment of the jump conditions that arise at moving material interfaces is intrinsic to the method. Extensions of the method to compressible flow, as well as adaptive and parallel implementations are under investigation.