A lagrangian method for calculating the dynamics of an incompressible fluid with free surface

Hirt, C.W.; Cook, J.L.; Butler, T.A.

doi:10.1016/0021-9991(70)90055-0

Cited by 145 publications

(55 citation statements)

References 12 publications

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“…The strictly Lagrangian algorithm was used in Hirt et al (1970) together with the finite-volume and in Okamoto & Kawahara (1990) with the finite-element method. In Fritts & Boris (1979) and Fyfe et al (1988) the free Lagrangian method with remeshing/rezoning was employed, the meshless particulate Lagrangian approach was advocated in Monaghan (1994), Morris (2000) (the Smoothed Particle Hydrodynamics (SPH) method) and the Boltzmann lattice-gas algorithm was addressed in Rothman & Zaleski (1997).…”

Section: Introductionmentioning

confidence: 99%

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Smolianski

2005

Int. J. Numer. Meth. Fluids

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The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modeling of twofluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the computational method.

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Section: Introductionmentioning

confidence: 99%

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Smolianski

2005

Int. J. Numer. Meth. Fluids

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“…[1][2][3][4] Specifically, the normal and the tangential stress conditions affect the accuracy of the free surface motion. The following equations have to be satisfied simultaneously on the free surfaces.…”

Section: Boundary Conditions and Phase Change Heatmentioning

confidence: 99%

“…As a result, a number of studies have been reported on the applications of mold filling or solidification in the casting processes. The conventional mold filling models are mostly based on the explicit scheme and their solution algorithms are SMAC or SOLA, [1][2][3][4] while the most solidification models are based in the implicit scheme. [5][6][7][8][9][10][11] If the filling process is only considered, the implicit scheme does not have much beneficial since it needs more time to finish the calculation than the explicit scheme when the same time steps are applied.…”

Section: Introductionmentioning

confidence: 99%

Development of a New Simulation Method of Mold Filling and Solidification Based on the SIMPLER Algorithm

2003

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A new combined method is to be introduced and applied to the mold filling and solidification process. In the present method, the SIMPLER algorithm was adopted to solve the momentum and energy equations. The VOF (Volume of Fluid) method was also adopted to track the free surfaces in the filling process and the Equivalent Specific Heat Method to solve the phase change heat transfer problem in the solidification process. The staggered grid system was used to prevent the false velocity field and the non-uniform control volumes were used to improve the efficiency of calculation. The standard DAFA (donor and acceptor flux approximation) method was adopted in the VOF method. In order to verify the new combined method, the numerical results were compared with the experimental results of mold filling and other simulation methods. It is concluded that the new method can be used as an effective simulation method for the simulation of mold filling and solidification in the casting processes.

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“…These can be classified into two main groups: interface-tracking and interface-capturing methods. On the one hand, the interface-tracking approaches chase the interface as it moves: (1) defining the interface as a boundary between subdomains of a moving mesh [1,2,3]; (2) following the Lagrangian trajectories of massless particles [4,5,6]. On the other hand, the interface-capturing approaches describe the motion of the interface by embedding the different fluids into a static mesh.…”

Section: Introductionmentioning

confidence: 99%

Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

Jofre

Borrell

Lehmkuhl

et al. 2015

Journal of Computational Physics

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UPCommonsPortal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Abstract: Volume-of-Fluid (VOF) is one of the methods of choice to reproduce the interface motion in the simulation of multi-fluid flows. One of its main strengths is its accuracy in capturing sharp interface geometries, although requiring for it a number of geometric calculations. Under these circumstances, achieving parallel performance on current supercomputers is a must. The main obstacle for the parallelization is that the computing costs are concentrated only in the discrete elements that lie on the interface between fluids. Consequently, if the interface is not homogeneously distributed throughout the domain, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. In this paper, we present a new parallelization strategy for general unstructured VOF solvers, based on a dynamic load balancing process complementary to the underlying DD. Its parallel efficiency has been analyzed and compared to the DD one using up to 1024 CPU-cores on an Intel SandyBridge based supercomputer. The results obtained on the solution of several artificially generated test cases show a speedup of up to 12x with respect to the standard DD, depending on the interface size, the initial distribution and the number of parallel processes engaged. Moreover, the new parallelization strategy presented is of general purpose, therefore, it could be used to parallelize any VOF solver without requiring changes on the coupled flow solver. Finally, note that although designed for the VOF method, our approach could be easily adapted to other interface-capturing methods, such as the Level-Set, which may present similar workload imbalances. SUMMARY OF CHANGESAccordingly to the comments raised by the reviewer, the changes on the manuscript are:1. As suggested by Reviewer #1: (1) Eq. 3 is valid only for divergence-free velocity fields, hence, this condition has been introduced in the text; (2) the limits of the sum in the numerator of Eqs. 9 -11 were incorrect, therefore, they have been corrected to start at 0 and end at P-1; (3) the description of Fig. 10 has been improved.2. The reviewer observed that Alg. 4 did not scale in terms of memory, since vector WI gathered information from all processes and, thus, grew with the size of the problem and number of CPU-cores. This may had become a bottleneck on larger scale tests. Therefore, we have developed a new version of the algorithm overcoming such limitations. The new version is based on non-blocking point-to-point communications.The new algorithm has substituted the previous one on the manuscript, and all tests for the LB strategy have been repeated and the results updated. Since Alg. 4 represents only 5% of the algorithm time, its upgrading has provided rather small improvements on the results. Even so, the important point is that the memory bottleneck has been eliminated.3. Furthermore, we have corrected some minor errors and we have tried to improve the wording across all the manuscrip...

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A lagrangian method for calculating the dynamics of an incompressible fluid with free surface

Cited by 145 publications

References 12 publications

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Development of a New Simulation Method of Mold Filling and Solidification Based on the SIMPLER Algorithm

Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

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