A parallel second-order unstructured finite volume method for 3D free-surface flows using a σ coordinate

Miguel Uh Zapata*, Wei Zhang, Damien Pham Van Bang, Kim Dan Nguyen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we introduce a second-order time- and space-accurate technique, developed to solve in parallel free-surface flows in arbitrary three-dimensional geometries. The discretization is based on a second-order finite-volume technique on prisms elements, consisting of triangular grids on the horizontal and bounded by a free surface and an irregular bottom on the vertical. The equations are transformed vertically to the σ-coordinate system in order to obtain an accurate representation of top and bottom topography. The reconstruction of three presure/velocity decoupling methods using a Crank-Nicolson scheme formulation is proposed. The Momentum Interpolation Method (MIM) is combined with Local Extremum Diminishing (LED) second-order upstream scheme for convective terms is developed. The parallelization is designed by a block domain decomposition technique. The discretization results in non-symmetric variable-coefficient linear systems which are solved using a parallel multi-color Successive Over-Relaxation algorithm. Several test cases of surface wave motion are used to demonstrate the capabilities, numerical stability and performance of the model.

Original languageEnglish
Pages (from-to)15-29
Number of pages15
JournalComputers and Fluids
Volume190
DOIs
Publication statusPublished - 15 Aug 2019
Externally publishedYes

Keywords

  • 3D Navier–Stokes equations
  • Finite volume method
  • Multi-color SOR method
  • Parallel
  • Projection method
  • Unstructured grid
  • σ Transformation

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