Local Discontinuous Galerkin Methods for the Khokhlov–Zabolotskaya–Kuznetzov Equation

Ching Shan Chou, Weizhou Sun, Yulong Xing, He Yang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation is a model that describes the propagation of the ultrasound beams in the thermoviscous fluid. It contains a nonlocal diffraction term, an absorption term and a nonlinear term. Accurate numerical methods to simulate the KZK equation are important to its broad applications in medical ultrasound simulations. In this paper, we propose a local discontinuous Galerkin method to solve the KZK equation. We prove the L2 stability of our scheme and conduct a series of numerical experiments including the focused circular short tone burst excitation and the propagation of unfocused sound beams, which show that our scheme leads to accurate solutions and performs better than the benchmark solutions in the literature.

Original languageEnglish (US)
Pages (from-to)593-616
Number of pages24
JournalJournal of Scientific Computing
Volume73
Issue number2-3
DOIs
StatePublished - Dec 1 2017
Externally publishedYes

Fingerprint

Local Discontinuous Galerkin Method
Galerkin methods
Ultrasonics
Ultrasound
Term
Propagation
Numerical methods
Diffraction
Acoustic waves
Burst
Fluids
Absorption
Excitation
Numerical Methods
Numerical Experiment
Benchmark
Fluid
Series
Experiments
Simulation

Keywords

  • KZK equation
  • Local discontinuous Galerkin method
  • Stability analysis

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

Cite this

Local Discontinuous Galerkin Methods for the Khokhlov–Zabolotskaya–Kuznetzov Equation. / Chou, Ching Shan; Sun, Weizhou; Xing, Yulong; Yang, He.

In: Journal of Scientific Computing, Vol. 73, No. 2-3, 01.12.2017, p. 593-616.

Research output: Contribution to journalArticle

Chou, Ching Shan ; Sun, Weizhou ; Xing, Yulong ; Yang, He. / Local Discontinuous Galerkin Methods for the Khokhlov–Zabolotskaya–Kuznetzov Equation. In: Journal of Scientific Computing. 2017 ; Vol. 73, No. 2-3. pp. 593-616.
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