A volume-of-fluid interface reconstruction algorithm that is second-order accurate in the max norm

With the increasing heterogeneity and on-node parallelism of high-performance computing hardware, a major challenge to computational physicists is to work in close collaboration with computer scientists to develop portable and efficient algorithms and software. The objective of our work is to implement a portable code to perform interface reconstruction using NVIDIA’s Thrust library. Interface reconstruction is a technique commonly used in volume tracking methods for simulations of interfacial flows. For that, we have designed a two-dimensional mesh data structure that is easily mapped to the 1D vectors used by Thrust and at the same time is simple to work with using familiar data structures terminology (such as cell, vertices and edges). With this new data structure in place, we have implemented a recursive volume-of-fluid initialization algorithm and a standard piecewise interface reconstruction algorithm. Our interface reconstruction algorithm makes use of a table look-up to easily identify all intersection cases, as this design is efficient on parallel architectures such as GPUs. Finally, we report performance results which show that a single implementation of these algorithms can be compiled to multiple backends (specifically, multi-core CPUs, NVIDIA GPUs, and Intel Xeon Phi coprocessors), making efficient use of the available parallelism on each.

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Volume of fluid interface reconstruction methods for multi-material problems

Applied Mechanics Reviews ◽

10.1115/1.1448524 ◽

2002 ◽

Vol 55 (2) ◽

pp. 151-165 ◽

Cited By ~ 89

Author(s):

David J Benson

Keyword(s):

Volume Of Fluid ◽

Review Article ◽

Arbitrary Lagrangian Eulerian ◽

Fluid Interface ◽

Reconstruction Methods ◽

Interface Reconstruction

Volume of fluid interface reconstruction methods are used to resolve the interfaces between different materials in Eulerian and arbitrary Lagrangian Eulerian calculations. Their accuracy is critical to the overall accuracy of the calculation since the interfaces define the interactions between adjacent materials. The methods have evolved since the early 1960s, and the early criticisms of them no longer hold. In this review article, the differences between the methods and their relative strengths are reviewed, and 38 reference sources are used.

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Chirp Reconstruction Algorithm for Generalized Second-Order Reed-Muller Frames

10.1109/itw48936.2021.9611492 ◽

2021 ◽

Author(s):

Renaud-Alexandre Pitaval ◽

Yi Qin

Keyword(s):

Reconstruction Algorithm ◽

Second Order

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A Volume-of-Fluid Based Numerical Simulation of Solidification in Binary Alloys on Fixed Non-Uniform Co-Located Grids

ASME 2009 International Manufacturing Science and Engineering Conference, Volume 1 ◽

10.1115/msec2009-84239 ◽

2009 ◽

Author(s):

Mehdi Farrokhnejad ◽

Anthony G. Straatman ◽

Jeffrey T. Wood

Keyword(s):

Volume Fraction ◽

Binary Alloys ◽

Solidification Process ◽

Casting Process ◽

Reconstruction Algorithm ◽

Volume Of Fluid ◽

Mold Filling ◽

Mg Alloys ◽

Uniform Grid ◽

Spurious Currents

In this paper, the authors present a platform for the modeling of mold filling and solidification of binary alloys with properties similar to Mg alloys. A volume-of-fluid (VOF) based method is used to capture the interface between solid and liquid in binary alloys solidification process on a fixed non-uniform grid, developed for implementation in a colocated finite volume framework. Contrary to other works, to update the volume fraction (of fluid) in the field, a link between source-based type of energy equation and VOF reconstruction algorithm is described and implemented. A new approximation to the pressure gradient is presented to remove all ‘Spurious Currents’ [1] resulting from pressure jumps in the vicinity of the interface. Based upon the work presented, it is concluded that the present combination of the equations are not only computationally straightforward to implement and upgrade to a 3D problem, but also provides an excellent platform to capture the interface between constituents in a die-casting process including solidification and mold filling process. The current framework will be used in future works to characterize the local mechanical properties of Mg alloys by using information from simulation at the dendritic level.

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3-D numerical modelling of crustal polydiapirs with volume-of-fluid methods

Geophysical Journal International ◽

10.1093/gji/ggaa141 ◽

2020 ◽

Vol 222 (1) ◽

pp. 474-506

Author(s):

Aurélie Louis-Napoléon ◽

Muriel Gerbault ◽

Thomas Bonometti ◽

Cédric Thieulot ◽

Roland Martin ◽

...

Keyword(s):

Volume Of Fluid ◽

Vof Method ◽

Earth’S Crust ◽

Gravitational Instabilities ◽

Interface Reconstruction ◽

Rayleigh Taylor Instability ◽

Earth's Crust ◽

Two Stages ◽

Rayleigh Benard ◽

Earth Dynamics

SUMMARY Gravitational instabilities exert a crucial role on the Earth dynamics and in particular on its differentiation. The Earth’s crust can be considered as a multilayered fluid with different densities and viscosities, which may become unstable in particular with variations in temperature. With the specific aim to quantify crustal scale polydiapiric instabilities, we test here two codes, JADIM and OpenFOAM, which use a volume-of-fluid (VOF) method without interface reconstruction, and compare them with the geodynamics community code ASPECT, which uses a tracking algorithm based on compositional fields. The VOF method is well-known to preserve strongly deforming interfaces. Both JADIM and OpenFOAM are first tested against documented two and three-layer Rayleigh–Taylor instability configurations in 2-D and 3-D. 2-D and 3-D results show diapiric growth rates that fit the analytical theory and are found to be slightly more accurate than those obtained with ASPECT. We subsequently compare the results from VOF simulations with previously published Rayleigh–Bénard analogue and numerical experiments. We show that the VOF method is a robust method adapted to the study of diapirism and convection in the Earth’s crust, although it is not computationally as fast as ASPECT. OpenFOAM is found to run faster than, and conserve mass as well as JADIM. Finally, we provide a preliminary application to the polydiapiric dynamics of the orogenic crust of Naxos Island (Greece) at about 16 Myr, and propose a two-stages scenario of convection and diapirism. The timing and dimensions of the modelled gravitational instabilities not only corroborate previous estimates of timing and dimensions associated to the dynamics of this hot crustal domain, but also bring preliminary insight on its rheological and tectonic contexts.

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