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 understand ing 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.

The one-dimensional, unsteady flow, flexible vessel computer simulation used in the past to study specific parts of the arterial system has now been extended to a whole-body simulation. This extension provides a better representation of the system hemodynamics because of the extensive interaction between all parts of the system via pressure and flow wave propagation. Current work centers on the cerebral circulation and on the ability of the simulations to provide neurosurgeons with the detailed information needed to plan for optimal surgical interventions or reconstructions. Coronary circulation dynamics are currently under study, with special attention being given to the role played by collaterals.

This project involves the acquisition and development of hardware and software systems for computer visualization of numerical and experimental data sets in support of machining process research. The objective is to develop a shared visualization resource to enhance the activities of various manufacturing research projects at UIUC. A state-of-the-art graphics workstation was obtained to support real-time animation of complex data sets. A combination of commercially available and custom software is used to meet the specific needs of the machining research projects.

Machine-tool selection and process design currently require expensive testing and time-consuming trial-and-error design methods. This project involves a collaboration between researchers in process simulation, computational mechanics, sensitivity analysis, and mechanistic modeling. New finite-element methods for simulating machining processes, including the three-dimensional effects of oblique processes were developed. These can be combined with sensitivity analysis to replace trial-and-error design procedures, to assess process robustness, and for material parameter identification. Numerical simulation and mechanistic modeling can be combined to reduce the need for expensive testing during model calibration.

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 stress-enhanced crack growth at elevated temperatures. A new space-time finite-element formulation supports continuous models of crack extension and evolving phase boundaries, including the effects of strain-enhanced diffusion. Adaptive analysis methods control solution error and provide the geometric flexibility to handle curved crack paths. Our current emphasis is on oxidation-induced cracking in nickel-based superalloys. Experimental studies will be used to calibrate 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 will address the special equation-solving requirements arising from the hyperbolic-elliptic structure of the space-time formulation. Automatic sequencing algorithms to support element-by-element solution procedures, the impact of coupling on the sparse structure, direct and iterative solution procedures, and parallel solution strategies will be investigated.

Variable-topology shape optimization is useful in design applications where holes can reduce weight without adversely affecting performance. Emerging applications of this technology include optimal design of microscopic manipulators, piezoelectric transducers and microstructures for functionally graded materials. Our work involves analytical and computational approaches to this class of problems, where the absence of a priori definition of the connectivity complicates the solution. We introduce a new formulation, incorporating a control on perimeter, that resolves a fundamental problem of ill-posedness in topology design problems. This leads to effective finite- element design procedures that are useful in practical design applications.

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 level-set method has been developed to propagate multidimensional detonation and shock fronts. Complex multisurfaced and multimaterial interactions can be handled in three-dimensional verification of asymptotic theory, and comparison with direct numerical simulation is being carried out. A simple method that uses level-set technology has been developed to solve Whitham's geometrical shock dynamics.