TY - JOUR
T1 - A parallel second-order unstructured finite volume method for 3D free-surface flows using a σ coordinate
AU - Uh Zapata, Miguel
AU - Zhang, Wei
AU - Pham Van Bang, Damien
AU - Nguyen, Kim Dan
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/8/15
Y1 - 2019/8/15
N2 - 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.
AB - 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.
KW - 3D Navier–Stokes equations
KW - Finite volume method
KW - Multi-color SOR method
KW - Parallel
KW - Projection method
KW - Unstructured grid
KW - σ Transformation
UR - http://www.scopus.com/inward/record.url?scp=85067005591&partnerID=8YFLogxK
U2 - 10.1016/j.compfluid.2019.06.001
DO - 10.1016/j.compfluid.2019.06.001
M3 - Article
AN - SCOPUS:85067005591
SN - 0045-7930
VL - 190
SP - 15
EP - 29
JO - Computers and Fluids
JF - Computers and Fluids
ER -