Simulation of Mantle Convection
S. Balachandar,* D. A. Yuen,* T. A. Cortese
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,* M. Y. Ha,* 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. Here we will develop and perform large-eddy simulation of flow in a simple stirred-tank reactor. The results will be compared with those obtained from particle-image velocimetry and laser-Doppler velocimetry measurements.

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.

Center for Process Simulation and Design
R. B. Haber,* J. A. Dantzig (Mech. & Indus. Engr.), H. Edelsbrunner (Comput. Sci.), 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. S
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 recrystallization and 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.

Process Modeling and Optimization for Crashworthiness of Extruded Aluminum Components
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.), N. Sobh, J. Huang, R. W. Hyland, Jr. (Alcoa), J. Teply (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 the process and product designs. To achieve this goal, researchers at the University of Illinois are developing macroscopic simulations of extrusion and quence processes with embedded microstructure evolution models. These predict densities of grain-boundary precipitates, crystallographic texture, recrystallization, and residual stress. The simulations are based on novel space-time finite-element models with discontinuous Galerkin formulations. Nonlinear programming is used to optimize process parameters and tool geometry to achieve improved performance. For example, quench process parameters can be optimized to obtain favorable precipitate distributions that limit microcracking under crash conditions.

Solid-Fluid Integration in Numerical Simulation of Solid-Fuel Rocket Engines
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.), N. Sobh, A. Acharya, J. Palaniappah, L. Yin
DOE Center for Simulation of Advanced Rockets

This project is part of the center's effort to develop computational technologies for large-scale, multiphysics simulations of solid-fuel rocket engines. In particular, the project addresses the problem of interfacing solid mechanics simulations of propellant and casing structures with simulations of combustion and turbulent flow. Space-time finite-element models are under development to represent time-varying material domains due to combustion and to support time-dependent mesh adaptation. Weak representations of the Robin-type jump conditions that arise from sharp-interface combustion models provide a basis for coupling the solid and fluid domains. Finite-element tearing and interconnecting types of domain decomposition techniques will be used to develop scalable solution algorithms.

Combustion-driven Fracture and Debonding in Solid-Fuel Rocket Engines
R. B. Haber,* P. H. Geubelle* (Aero. & Astro. Engr.)
DOE Center for Simulation of Advanced Rockets

This work is part of the center's effort to develop computational technologies for large-scale multiphysics simulations of solid-fuel rocket engines. The focus is on simulations of fracture in solid-fuel engines at the meso-scale (i.e., pertaining to length scales associated with the propellant grain structure). Simulations will be based on cohesive fracture models implemented in adaptive finite-element codes. 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 internal combustion process.

Intergranular Fracture and Oxygen Embrittlement in a Viscoplastic Solid
R. B. Haber,* F. L . Carranza, J. Telesman (NASA Lewis Res. Center)
National Aeronautics and Space Administration, NGT 70374; University of Illinois

Control of creep and fatigue crack growth in high-temperature engine components is a key enabling technology for the next generation of high-performance aircraft. This project involves numerical studies of oxidation-driven crack growth at elevated temperatures. An adaptive space-time finite-element formulation models transient and steady-state crack growth, including stress-enhanced grain-boundary diffusion of oxygen. A moving cohesive interface model provides a criterion for intergranular fracture. Results include new stability criteria for cohesive fracture models and extensive studies of intergranular fracture in a viscoplastic material under various load programs, with and without oxygen embrittlement.

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,* T. L. Jackson (CSAR)
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.

Program-Burn and Level-Set Technology
D. S. Stewart,* T. L. Jackson (CSAR), J. Bdzil (LANL)
Los Alamos National Laboratory, 673M0014-9

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.