No abstract

The Stokes equations are solved using spectral methods with staggered and nonstaggered grids. Numerous ways to avoid the problem of spurious pressure modes are presented, including new techniques using the pseudospectrdJ method and a method solving the weak form of the governing equations (a variatron on the "spectral element" method developed by Patera). The pseudospectral methods using nonstaggercd grids are simpler to implement and have comparable or better accuracy than the staggered grid formulations. Three test cases arc presented: a formulation with an exact solution, a formulation with homogeneous boundary conditions, and the driven cavity problem. The solution accuracy is shown to be greatly improved for the driven cavity problem when the analytical solution of the singular flow behavior in the upper corners is separated from the computatmnal solution.:(' ,991 Academic Press, 1°C

Engineering education agencies worldwide echo the need of graduating engineers to be aware of the societal context of engineering. Service learning is a viable pedagogy that can bring students to understand this dimension in a rather direct way. Undergraduate engineering students visited low-income households in their community and installed insulation materials on doors and windows, thereby reducing heating costs. The students calculated the resulting dollar amount of energy savings using heat transfer principles. A quantitative analyses of the reflections of the students clearly showed that they became more aware and sensitive to their roles as engineers in a societal context.

Fluid flow under a grinding wheel is modeled using a perturbation scheme. In this initial effort to understand the flow characteristics, we concentrate on the case of a smooth wheel with slight clearance between the wheel and workpiece. The solution at lowest order is that given by standard lubrication theory. Higher-order terms correct for inertial and two-dimensional effects. Experimental and analytical pressure profiles are compared to test the validity of the model. Lubrication theory provides good agreement with low Reynolds number flows; the perturbation scheme provides reasonable agreement with moderate Reynolds number flows but fails at high Reynolds numbers. Results from experiments demonstrate that the ignored upstream and downstream conditions significantly affect the flow characteristics, implying that only a model based on the fully two- (or three-) dimensional Navier-Stokes equations will accurately predict the flow. We make one comparison between an experiment with a grinding wheel and the model incorporating a one-dimensional sinusoidal roughness term. For this case, lubrication theory surprisingly provides good agreement with experiment.

The pseudospectral method is used for the first time to solve the thermohydrodynamic lubrication equations for a slider bearing. The orthogonal polynomials used in the series expansions are Lagrangian interpola nts derived from a Legendre basis. Exponential convergence to exact solutions is demonstrated and favourable comparisons with previous work are made.