A spectrally accurate domain-decomposition methodology for direct numerical simulation of the wake behind rectangular bluff bodies has been developed. A hybrid-GMRES method has been developed to solve efficiently the resulting discretized linear system on the massively parallel Connection Machine CM5. Improved understanding of the three-dimensional wake behind a square cylinder is sought.

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.

A one-dimensional simulation of the arterial side of the cardiovascular system has been generated. Specific atten tion is being given to the cerebral circulation. To help in the conformation process, neurosurgeons are using miniature electronic flowmeters to measure blood flows in certain critical vessels. When these measured flows show deviances from the computer predictions, the terminal resistance patterns are adjusted to bring about conformity for that patient. When a general consensus pattern is achieved after many such adjustments, the computer model can be used with confidence to help in the planning of future surgical modifications and reconstructions.

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 UIUC will develop improved numerical models for extrusion and quenching processes that predict product shape and microstructure. An experimental program at Alcoa will calibrate and verify the process models, which will be integrated with existing crashworthiness models at Alcoa. Process parameters will be optimized to obtain favorable precipitate distributions in order to limit microcracking under crash loads.

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 and experimental studies of oxidation-driven crack growth at elevated temperatures. An adaptive space-time finite-element formulation models transient and steady-state crack growth, including the effects of stress-enhanced diffusion. A moving cohesive interface model provides a criterion for intergranular fracture. Our current emphasis is on oxidation-induced cracking in nickel-based superalloys. Experimental studies are planned to calibrate and verify the numerical model.

This work supplements a NASA-sponsored research project involving the development of a new space-time finite-element model for crack propagation. A collaboration between researchers in computational mechanics and computer science addresses the special equation-solving requirements arising from the hyperbolic-elliptic structure of the space-time formulation. Both direct and iterative solvers have been investigated. Automatic sequencing algorithms have been developed to support a highly efficient element-by-element solution procedure for the hyperbolic subproblem. This scheme provides a powerful and cost-effective preconditioner within a conjugate-gradient algorithm for the coupled hyperbolic-elliptic problem.

Computations involving the dynamic evolution of localized regions in materials whose response is characterized by a net softening effect offer a great challenge as far as numerical convergence is concerned. A finite-difference scheme is designed to integrate the system of nonlinear, coupled partial differential equations. Necessary conditions for numerical stability are derived analytically. Implementation of a recently developed energy criterion allows for a rationale by which numerical convergence can be judged. This rationale is used to design an efficient and robust adaptive scheme that automatically selects the temporal evolution increment that is sufficient to maintain numerical stability.

The purpose of this project is to formalize the concept of program burn, which is a numerical strategy used in detonation hydrocodes to replace the detonation reaction zone with a discrete heat-releasing algorithm on a pointwise mesh of the underlying code. The new strategies take advantage of recent advances in level-set methodology to predetermine burn times on a fixed mesh. Delta-function source terms are defined a priori and then are used to define a new singular partial differential equation, which serves as a model for the new system.