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

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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
Issue number2-3
StatePublished - Dec 1 2017
Externally publishedYes


  • KZK equation
  • Local discontinuous Galerkin method
  • Stability analysis

ASJC Scopus subject areas

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


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