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Numerical solution of the viscous surface wave with discontinuous Galerkin method

Lei Wu Brown University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25030

ESAIM: Mathematical Modelling and Numerical Analysis, 49, 1019-1046, 2015
We consider an incompressible viscous flow without surface tension in a finite-depth domain of two dimensions, with free top boundary and fixed bottom boundary. This system is governed by the Navier-Stokes equations in this moving domain and the transport equation on the moving boundary. In this paper, we construct a stable numerical scheme to simulate the evolution of this system by discontinuous Galerkin method, and discuss the error analysis of the fluid under certain assumptions. Our formulation is mainly based on the geometric structure introduced earlier in the literature, and the natural energy estimate, which is rarely used in the numerical study of this system before.
Stability, Free Boundary, Navier-Stokes equation
[ Download ] [ 2016-10-12 03:36:43 uploaded by chiwangshu ] [ 977 downloads ] [ 0 comments ] [ Cited by 2 ] 
@inproceedings{lei2015numerical,
  title={Numerical solution of the viscous surface wave with discontinuous Galerkin method},
  author={Lei Wu, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012033643028403148},
  booktitle={ESAIM: Mathematical Modelling and Numerical Analysis},
  volume={49},
  pages={1019-1046},
  year={2015},
}
Lei Wu, and Chi-Wang Shu. Numerical solution of the viscous surface wave with discontinuous Galerkin method. 2015. Vol. 49. In ESAIM: Mathematical Modelling and Numerical Analysis. pp.1019-1046. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012033643028403148.
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