Development of a super-grid-scale model for artificial boundaries in fluid dynamics and other wave pheonmena

California Institute Of Technology, Pasadena CA

Investigators

Abstract

A new framework for modeling artificial boundary conditions in a variety of applications, including fluid dynamics, acoustics, and electromagnetic wave propagation, will be developed. Previous approaches have relied either on simple descriptions of those processes occurring near boundaries, such as linearized disturbances to uniform states, or on a range of ad hoc techniques that attempt to mitigate spurious artifacts of domain truncation. The present work is based on the concept of a super-grid-scale model that is in many ways analogous to sub-grid-scale models that are used in Large Eddy Simulations of turbulent flows. The formulation explicitly recognizes that in general systems (especially inhomogeneous and nonlinear PDE), domain truncation, like filtering, is a modeling problem--the result is ``missing information'' that cannot be recovered from first principles. Many existing techniques (especially damping layers) implicitly supply such a model, but our hypothesis, backed by preliminary calculations in compressible flow and acoustic applications, is that better models can be developed by exploiting a strong analogy with sub-grid-scale modeling techniques. The analogy is based on the dual roles that filtering and windowing play in real and Fourier space. The proposal details a rationally sequenced research program that includes examination of several different super-grid models (based on analogies to existing sub-grid models), detailed computations and comparison with previous methods in the areas of incompressible and compressible flow, acoustics, and electromagnetic, and detailed analysis of stability and convergence of the models and discretized systems. It is often said that simulation is becoming the 'third leg' of science, taking an important place beside theory and experiment. In engineering, simulation is an essential tool that enables design and optimization based on first-principles rather than empirical correlations. However, computation is only useful when the underlying system is correctly modeled. Indeed, many relevant systems in fluid dynamics, acoustics, and electromagnetic waves cannot be reliably simulated with existing techniques. Techniques for artificial domain truncation, in particular, are a pacing item in many applications in these and related fields. Artificial domain truncation (or artificial boundary conditions) refers to situations where one wishes to simulate only a portion of a larger system in order to reduce computational effort. The present research will provide a new generation of such techniques that are based on a rigorous and well-validated modeling framework called the super-grid-scale model. Successful outcome of the proposed research has potential for far-ranging impact scientific and engineering design-oriented simulations.