Date of Award

Spring 1-1-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical Engineering

First Advisor

Oleg V. Vasilyev

Second Advisor

Daven Henze

Abstract

The problem of computational aeroacoustic modelling is complex and of practical interest, especially for external flows around arbitrary geometries. Aeroacoustic interactions are more sensitive to errors than aerodynamics, and as such, particular care must be taken to accurately and efficiently model them.

For efficiency, an adaptive multi-resolution grid is used to reduce the number of grid points while still resolving pertinent scales. The compressible Navier-Stokes equations are solved using the Adaptive Wavelet Collocation Method (AWCM), where wavelet decomposition provides a fast and efficient method for grid compression while maintaining rigorous control over the error.

The primary focus of this thesis is developing methodologies for efficient handling of solid obstacles within flows. Proper modelling of arbitrarily shaped obstacles is a prominent issue for fluid simulation, for which there are several approaches. Immersed boundary methods are well suited for use with rectilinear grids as they circumvent the need for a body-conformal mesh and allow curved geometry. The geometry can be efficiently generated through external CAD software, and ray-tracing algorithms used to create accurate masking functions. Ray-tracing is attractive for parallel computational systems as each grid point can be analyzed independently. A masking function provides the geometry definition for volume penalization methods.

A new volume penalization method is introduced here to address several difficulties associated with the Brinkman Penalization Method (BPM). Brinkman penalization is generally limited to a select group of fluid problems, and is greatly restricted in the handling and types of boundary conditions. To overcome these issues, a new, characteristic-based volume penalization method is proposed, allowing for general Dirichlet and Neumann boundary conditions to be defined.

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