A computationally efficient 3D finite‐volume scheme for violent liquid–gas sloshing

Abstract

Summary We describe a semi‐implicit volume‐of‐fluid free‐surface‐modelling methodology for flow problems involving violent free‐surface motion. For efficient computation, a hybrid‐unstructured edge‐based vertex‐centred finite volume discretisation is employed, while the solution methodology is entirely matrix free. Pressures are solved using a matrix‐free preconditioned generalised minimum residual algorithm and explicit time‐stepping is employed for the momentum and interface‐tracking equations. The high resolution artificial compressive (HiRAC) volume‐of‐fluid method is used for accurate capturing of the free surface in violent flow regimes while allowing natural applicability to hybrid‐unstructured meshes. The code is parallelised for solution on distributed‐memory architectures and evaluated against 2D and 3D benchmark problems. Good parallel scaling is demonstrated, with almost linear speed‐up down to 6000 cells per core. Finally, the code is applied to an industrial‐type problem involving resonant excitation of a fuel tank, and a comparison with experimental results is made in this violent sloshing regime. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical Simulation of Liquid Sloshing with Different Filling Levels Using OpenFOAM and Experimental Validation

“…Ramaswamy et al [16] studied 2D viscous flow sloshing by using the Lagrange-finite element method. Oxtoby [17] described a semi-implicit volume-of-fluid (VOF) free surface modelling methodology for flow problems involving violent free-surface motions. Kishev et al [18] developed a new Computational Fluid Dynamics (CFD) simulation approach based on the constraint interpolation profile (CIP) method to tackle the violent sloshing problem.…”

Numerical modelling of 3D sloshing experiments in rectangular tanks

“…Many efforts have been made to develop efficient algorithms to describe moving interfaces, 15 and different versions of very well known techniques are available to properly describe long-term free surface problems. The volume of fluid [16,17,9,18], level set (LS) [19,20], Eulerian-Lagrangian [21,22,23], and deforming domain [24,25] methods have been proposed to describe interface motions in the framework of different discretization schemes, i.e., finite differences, finite vol-20 umes, or finite element formulations. In addition, several techniques, such as smooth particle hydrodynamics [26], particle finite elements [27], and boundary elements [28], have been specifically developed or have been successfully applied to describe free surface flow problems [29].…”

An AMG strategy for efficient solution of free-surface flows

“…From the literature, a number of advanced sparse linear solvers have been applied to FSM for the purpose of solving the pressure correction equation. These include successive over-relaxation [9], preconditioned GMRES [10,8], various conjugate-gradient type methods [11,12,13,14,15] and geometric multigrid methods [16,17,18]. Other attempts at solution acceleration include improved initial condition prediction [19] and algebraic multigrid (AMG) methods [20].…”

“…In the case of the implicit pressure formulation, the latter involves the solution of a large, sparse and asymmetric linear system of equations. At present, this is effected by means of a pre-conditioned generalised minimal residual (GMRES) solver (Malan et al, 2007;Heyns et al, 2013;Oxtoby et al, 2015). Though this solver was demonstrated to be exceptionally efficient it was found to consume up to 95 per cent computational time.…”

“…From the literature, a number of advanced sparse linear solvers have been applied to FSM for the purpose of solving the pressure correction equation. These include successive over-relaxation (Kurioka and Dowling, 2009), pre-conditioned GMRES (Lee et al, 2005;Oxtoby et al, 2015), various conjugate-gradient type methods (Van der Vorst, 1992;Koçyigit et al, 2002;Soto et al, 2003;Aubry et al, 2008;Štrubelj et al, 2009) and geometric multigrid methods (Farmer et al, 1994;Waltz and Löhner, 2000;Popinet, 2003). Other attempts at solution acceleration include improved initial condition prediction (Löhner, 2005) and algebraic multigrid (AMG) methods (Kim and Moin, 2009).…”