An explicit method for numerical simulation of wave motion---1-D wave motion

Zhenpeng Liao, Heng Liu, Zhinan Xie

doi:10.6052/0459-1879-2009-3-2007-635

Volume 41 Issue 3

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Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2009 > 41(3): 350-360

Zhenpeng Liao, Heng Liu, Zhinan Xie. An explicit method for numerical simulation of wave motion---1-D wave motion[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3): 350-360. doi: 10.6052/0459-1879-2009-3-2007-635

Citation:

Zhenpeng Liao, Heng Liu, Zhinan Xie. An explicit method for numerical simulation of wave motion---1-D wave motion[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3): 350-360. doi: 10.6052/0459-1879-2009-3-2007-635

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An explicit method for numerical simulation of wave motion---1-D wave motion

doi: 10.6052/0459-1879-2009-3-2007-635

Zhenpeng Liao, Heng Liu, Zhinan Xie

Institute of Engineering Mechanics, SSB, Harbin 150080, ChinaInstitute of Engineering Mechanics, SSB, Harbin 150080, ChinaInstitute of Engineering Mechanics, SSB, Harbin 150080, China

Received Date: 2007-12-19
Rev Recd Date: 2008-03-10
Publish Date: 2009-05-18

Abstract

Abstract

A new explicit method for numerical simulation of wave motion in time domainis first presented and illustrated by constructing the recursion formulas atnodal points of an irregular grid for 1-D wave equation in this paper. Todemonstrate the possibility to develop stable and high-order formulas withthe method, accuracy and stability of the numerical simulation are firstdiscussed in detail for the 1-D scalar wave equation in a uniform grid, andan approach is then proposed to construct the stable formulas with 2M-orderaccuracy both in time and space. A theoretical case is illustrated byconstructing the formulas of second order (M=1) and fourth order (M=2). Theresults with the proposed method are validated by a series of numericaltests.
- wave equation,
- numerical simulation,
- explicit recursion formula,
- finite element method (FEM)