Performance Analysis of High-Order Numerical Methods for Time-Dependent Acoustic Field Modeling

  • Pedro Henrique Rocha Moy

Student thesis: Master's Thesis

Abstract

The discretization of time-dependent wave propagation is plagued with dispersion in which the wavefield is perceived to travel with an erroneous velocity. To remediate the problem, simulations are run on dense and computationally expensive grids yielding plausible approximate solutions. This work introduces an error analysis tool which can be used to obtain optimal simulation parameters that account for mesh size, orders of spatial and temporal discretizations, angles of propagation, temporal stability conditions (usually referred to as CFL conditions), and time of propagation. The classical criteria of 10-15 nodes per wavelength for second-order finite differences, and 4-5 nodes per wavelength for fourth-order spectral elements are shown to be unrealistic and overly-optimistic simulation parameters for different propagation times. This work analyzes finite differences, spectral elements, optimally-blended spectral elements, and isogeometric analysis.
Date of AwardJul 2012
Original languageEnglish (US)
Awarding Institution
  • Physical Science and Engineering
SupervisorVictor Calo (Supervisor)

Keywords

  • Dispersion
  • Finite Elements
  • Wave Propagation
  • Wave Equation
  • Spectral Elements
  • Isogeometric Analysis

Cite this

'