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SUMMARY With the aim of accurately modelling free‐surface flow of two immiscible fluids, this study presents the development of a new volume‐of‐fluid free‐surface capturing formulation. By building on existing volume‐of‐fluid approaches, the new formulation combines a blended higher resolution scheme with the addition of an artificial compressive term to the volume‐of‐fluid equation. This reduces the numerical smearing of the interface associated with explicit higher resolution schemes while limiting the contribution of the artificial compressive term to ensure the integrity of the interface shape is maintained. Furthermore, the computational efficiency of the the higher resolution scheme is improved through the reformulation of the normalised variable approach and the implementation of a new higher resolution blending function. The volume‐of‐fluid equation is discretised via an unstructured vertex‐centred finite volume method and solved via a Jacobian‐type dual time‐stepping approach. Copyright © 2012 John Wiley & Sons, Ltd.

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.

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This study presents the development of novel modelling technology for compressible and violent free-surface flows, where the new technology aims to extend the capabilities of existing FSM formulations. For the purpose of this study the volume-of-fluid (VOF) method is extended in two ways: Firstly, we aim to improve on the accuracy of existing free-surface interface capturing schemes, and secondly, a newly developed weakly compressible formulation is introduced. The proposed interface capturing formulation reduces the degree of numerical smearing, while maintaining the integrity of the interface shape. It involves combining the approaches of blended higher-resolution discretisation and adding an artificial compressive term in a manner which retains the strength of each. The weakly compressible formulation proposes an altered governing equation set which accurately accounts for large variance in gas density at low Mach numbers and may be solved at little additional computational cost. All governing equations are discretized via an unstructured edge-based vertex centred finite volume method, and solved via a parallel implicit solver. The newly developed technology is validated through application to various benchmark test cases.