IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Two numerical approaches for predictions of physical fields in complex geometries at local scales

  • Nov. 27, 2012
  • 2:30 p.m.
  • LeConte 312

Abstract

In this talk, two approaches will be presented for some multiphysics problems: flow-generated sound generation and propagation, energy conversion and storage systems, and uncharged/charged particulate systems. For these problems, it is crucial to resolve complex geometries at local scales, because many important processes occur at the local region around complex geometries.

The first is called Brinkman penalization method, which can be used for efficient representation of complex geometries to model flow-generated sound generation and propagation in a complex physical environment. The method was developed for compressible flows around solid obstacles of complex geometries. It is the first consistent Immersed Boundary Method for compressible flows. This method is based on a physically sound mathematical model for compressible flows through porous media.

The second is called Physalis method, which has been developed for predictions of fluid, electric, and thermal fields in heterogeneous materials for applications in energy conversion and storage systems, and uncharged/charged particulate systems. The idea of creating a cage around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. We will discuss our approach as a foundation for the application of this approach to the determination of local behavior in heterogeneous functional materials, for example, the distribution of electric charge. The most common approach to representing the multi-physics of the functionality of these materials is to construct average or “effective” property approximations. This approach is approximate at best, teaches us little about the local physics, and loses the subtleties of the local geometries and morphology. Perhaps the most serious loss in this approach is the failure of such a model to tell us how to construct and synthesize such a material system, using the physics as a guide at the local level. Our approach provides a local representation that can recover the physics and the morphology as a foundation for understanding and synthesis.

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