Analytical and geometrical tools for 3D volume of fluid methods in general grids

López, J.; Hernández, J.

doi:10.1016/j.jcp.2008.03.010

Cited by 74 publications

(87 citation statements)

References 15 publications

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“…The final calculation step to obtain the value of C , which can be solved iteratively using, for example, Brent's method, or analytically, in an approach that increases the computational efficiency of the interface reconstruction method. In this work, an improved version of the analytical method proposed in [15], which can also be applied to general convex grids, is presented.…”

Section: Introductionmentioning

confidence: 99%

“…The first analytical approach valid for general convex grids in both two and three dimensions was proposed by López and Hernández [15]. They used an improved bracketing procedure based on a centered sequential search for cells with a total number of vertices I p ≤ 8 and a binary searching otherwise, and proposed an analytical method to solve the inverse problem C = C (V T ).…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Diot et al [6] proposed an efficient approach for general 2D and axisymmetric geometries, which is based on using an analytical formula for both the bracketing and final calculation steps of the volume enforcement problem, as in [12,22]. The main difference with the 2D version of the method proposed in [15] lies in the way the areas of the truncated polygons are calculated in the bracketing step. In [6], the cell is decomposed into trapezoidal elements and the areas of the successively truncated polygons are computed in an additive way from the trapezoids areas, for which an exact formula is proposed, whereas in [15] the whole area of every truncated polygon is computed, regardless of whether or not it contains subpolygons of previously computed areas.…”

Section: Introductionmentioning

confidence: 99%

“…These techniques are combined in a new method to enforce volume conservation, which does not require the sequential polyhedra truncation operations typically used in standard methods. The new methods have been implemented into existing geometrical routines described in López and Hernández [15], which are further improved by using more efficient formulae to compute areas and volumes of general convex 2 and 3D polytopes. Different tests using regular and irregular cell geometries are carried out to demonstrate the robustness and substantial improvement in computational efficiency of the proposed techniques, which increase the computation speed of the mentioned routines by up to 3 times for the 3D problems considered in this work.…”

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confidence: 99%

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A new volume conservation enforcement method for PLIC reconstruction in general convex grids

López

Hernández

Gómez

et al. 2016

Journal of Computational Physics

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A comprehensive study is made of methods for resolving the volume conservation enforcement problem in the PLIC reconstruction of an interface in general 3D convex grids. Different procedures to bracket the solution when solving the problem using previous standard methods are analyzed in detail. A new interpolation bracketing procedure and an improved analytical method to find the interface plane constant are proposed. These techniques are combined in a new method to enforce volume conservation, which does not require the sequential polyhedra truncation operations typically used in standard methods. The new methods have been implemented into existing geometrical routines described in López and Hernández [15], which are further improved by using more efficient formulae to compute areas and volumes of general convex 2 and 3D polytopes. Different tests using regular and irregular cell geometries are carried out to demonstrate the robustness and substantial improvement in computational efficiency of the proposed techniques, which increase the computation speed of the mentioned routines by up to 3 times for the 3D problems considered in this work.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A new volume conservation enforcement method for PLIC reconstruction in general convex grids

López

Hernández

Gómez

et al. 2016

Journal of Computational Physics

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“…Note that the basic geometric operation used in the first two steps is the truncation of a polyhedron by a plane. A general algorithm to perform it is described in the work by López et al [32].…”

Section: Interface Advectionmentioning

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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On estimating the interface normal and curvature in piecewise linear interface calculation‐volume of fluid approach for three‐dimensional arbitrary meshes

Amani

Muela

Schillaci³

et al. 2022

AIChE Journal

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Volume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC-generated planes in comparison with the exact interface, a point-cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3-dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.

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Analytical and geometrical tools for 3D volume of fluid methods in general grids

Cited by 74 publications

References 15 publications

A new volume conservation enforcement method for PLIC reconstruction in general convex grids

A new volume conservation enforcement method for PLIC reconstruction in general convex grids

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

On estimating the interface normal and curvature in piecewise linear interface calculation‐volume of fluid approach for three‐dimensional arbitrary meshes

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