Publications

We analyze the artificial dissipation introduced by a streamline-upwind Petrov-Galerkin finite element method and consider its effect on the conservation of total enthalpy for the Euler and laminar Navier-Stokes equations. We also consider the chemically reacting case. We demonstrate that in general, total enthalpy is not conserved for the important special case of the steady-state Euler equations. A modification to the artificial dissipation is proposed and shown to significantly improve the conservation of total enthalpy.

A common purpose for performing an aerodynamic analysis is to calculate the resulting loads on a solid body immersed in the flow. Pressure or heat loads are often of interest for characterizing the structural integrity or thermal survivability of the structure. This document describes two algorithms for tightly coupling the mass, momentum and energy conservation equations for a compressible fluid and the energy conservation equation for heat transfer through a solid. We categorize both approaches as monolithically coupled, where the conservation equations for the fluid and the solid are assembled into a single residual vector. Newton's method is then used to solve the resulting nonlinear system of equations. These approaches are in contrast to other popular coupling schemes such as staggered coupling methods were each discipline is solved individually and loads are passed between as boundary conditions, and demonstrates the viability of the monolithic approach for aeroheating problems.

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In this article we concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of `upwind' and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), `entropy' variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software, support such as those in the SANDIA National Laboratory framework SIERRA.