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Journal of Scientific Computing

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03-08-2017

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

Authors: Ching-Shan Chou, Weizhou Sun, Yulong Xing, He Yang

Published in: Journal of Scientific Computing | Issue 2-3/2017

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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 \(L^2\) 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.

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Title: Local Discontinuous Galerkin Methods for the Khokhlov–Zabolotskaya–Kuznetzov Equation
Authors: Ching-Shan Chou
Weizhou Sun
Yulong Xing
He Yang
Publication date: 03-08-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2-3/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0502-z

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