Reliability of first order numerical schemes for solving shallow water system over abrupt topography

Reliability of first order numerical schemes for solving shallow water system over abrupt topography. Morales de Luna, T., Díaz, Manuel J., C., & Parés, C. Applied Mathematics and Computation, 219(17):9012–9032, 2013.
abstract bibtex

Abstract We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed error depends on the method. Moreover, the solutions given by the numerical scheme can be significantly different if not enough space resolution is used. We shall pay special attention to the well-known hydrostatic reconstruction technique where it is shown that the effect of large bottom discontinuities might be missed and a modification is proposed to avoid this problem.

@Article{moralesdeluna13Reliability,
  author   = {Morales de Luna, Tom{\'a}s and Castro D{\'i}az, Manuel J. and Par{\'e}s, Carlos},
  title    = {{R}eliability of first order numerical schemes for solving shallow water system over abrupt topography},
  journal  = {Applied Mathematics and Computation},
  year     = {2013},
  volume   = {219},
  number   = {17},
  pages    = {9012--9032},
  abstract = {Abstract We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed error depends on the method. Moreover, the solutions given by the numerical scheme can be significantly different if not enough space resolution is used. We shall pay special attention to the well-known hydrostatic reconstruction technique where it is shown that the effect of large bottom discontinuities might be missed and a modification is proposed to avoid this problem.},
}

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