Stabilized edge‐based finite element simulation of free‐surface flows

Abstract

SUMMARYFree-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbours and coastal areas. The computation of such highly nonlinear flows is challenging since free-surfaces commonly present merging, fragmentation and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function which is transported in a flow field. In this work we present a three-dimensional parallel edge-based incompressible SUPG/PSPG finite element method to cope with free-surface problems with volume-of-fluid (VOF) extensions to track the evolving free surface. The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. We studied variants of this formulation, considering the effects of discontinuity capturing and a particular tangent transformation designed to increase interface sharpness. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method were tested with several validation problems.

A free surface finite element model for low Froude number mould filling problems on fixed meshes

“…We have observed that this mass loss can be reduced by increasing the Smagorinsky constant. The mass loss could also be corrected by slightly displacing the interface at each time step as suggested in [20,31]. As in the hollow mechanical piece, we have also included results obtained with the Eulerian two-phase flow model to see that after approximately 4 s the mass loss becomes so important that the results lose any sense.…”

Raw data queries during data-intensive parallel workflow execution

“…Specifically, this simulation analyzes the three-dimensional flow of an incompressible fluid in a cavity. This problem is a popular benchmark in CFD, used to evaluate new codes or new solution methods [18]. This benchmark is consistently used throughout this paper.…”

“…This case study uses EdgeCFD software and, consequently, the modeled workflow presents the same name (i.e., EdgeCFD workflow). EdgeCFD is a Fortran90 finite element application where the kernel of the computational solution consists of a fully implicit predictor -multicorrector time integration scheme as described in [18]. The generalized trapezoidal rule is employed in the time discretization, with an adaptive time stepping procedure based on a proportional-integral-derivative (PID) controller.…”

Stabilized edge‐based finite element computation of gravity currents in lock‐exchange configurations

“…More recently, Ribeiro et al [30] presented an edge-based implementation for stabilized semi-discrete and space-time finite element formulations for shallow water equations, Catabriga and Coutinho [31] for the implicit SUPG solution of the Euler equations, Soto et al [32] for incompressible flow problems with fractional step methods and Kraft et al [33] for a segregated symmetric stabilized solution of incompressible flow with heat transfer and the parallel simulation of viscoplastic and free surface flows [34,35]. It has been shown by Ribeiro and Coutinho [36] that, for unstructured grids composed by tetrahedra, edge-based data structures decrease the number of floating point operations and indirect addressings in matrix-vector products needed in the Krylov space solvers and diminish the storage area to hold Jacobians compared with element and pointwise data structures, particularly for problems involving many degrees of freedom.…”

“…It has been shown by Ribeiro and Coutinho [36] that, for unstructured grids composed by tetrahedra, edge-based data structures decrease the number of floating point operations and indirect addressings in matrix-vector products needed in the Krylov space solvers and diminish the storage area to hold Jacobians compared with element and pointwise data structures, particularly for problems involving many degrees of freedom. The construction of edge operations are completely algebraic [30,31,[33][34][35], based on the concept of disassembling element operators, regardless of the particular underlying finite element formulation, thus providing a fast platform for simulation of complex problems such as those found in the present work.…”