On mass-conserving least-squares methods

J. J. Heys, E. Lee, T. A. Manteuffel, S. F. Mccormick

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21 Citations (Scopus)

Abstract

Least-squares variational methods have several practical and theoretical advantages for solving elliptic partial differential equations, including symmetric positive definite discrete operators and a sharp error measure. One of the potential drawbacks, especially in three dimensions, is that mass conservation is achieved only in a least-squares sense, and underresolved solutions are especially vulnerable to poor conservation. For the stationary Navier-Stokes equations, which are typically rewritten as a larger system of first-order equations, the loss of mass in the approximate solution is strongly dependent upon the boundary conditions used. A new first-order system reformulation of the Navier-Stokes equations is presented that admits a wider range of mass-conserving boundary conditions. This new formulation is shown to provide both excellent mass conservation and excellent algebraic multigrid performance for three different problems, a square channel, backwardfacing step, and branching tubes with two generations of bifurcations.

Original languageEnglish
Pages (from-to)1675-1693
Number of pages19
JournalSIAM Journal on Scientific Computing
Volume28
Issue number5
DOIs
Publication statusPublished - 2006 Dec 1

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Heys, J. J., Lee, E., Manteuffel, T. A., & Mccormick, S. F. (2006). On mass-conserving least-squares methods. SIAM Journal on Scientific Computing, 28(5), 1675-1693. https://doi.org/10.1137/050640928