Reconstructing Volume Tracking
Citations
1,949 citations
Cites methods from "Reconstructing Volume Tracking"
...One can simply use a standard root-finding approach to find the particular value ofα at which the cut area has the desired value, for instance, an iterative method may be found in Rider & Kothe (1998)....
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...The more accurate techniques are now known as the piecewise linear interface construction (PLIC) method (Ashgriz & Poo 1991, Li 1995, Parker & Youngs 1992, Rider & Kothe 1995, Pilliod & Puckett 1997, Rudman 1997, 1998, Rider & Kothe 1998, Gueyffier et al 1998)....
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...First-order and second-order accurate algorithms have been developed by several authors (Collela 1990, Bell et al 1990, LeVeque 1996, Puckett et al 1997, Rider & Kothe 1998)....
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1,120 citations
Cites methods or result from "Reconstructing Volume Tracking"
...Numerical results based upon a series of two- and three-dimensional interface stretch tests proposed and inspired by Rider and Kothe [27, 28] are described to demonstrate that the new particle level set technique compares favorably with VOF methods with regard to mass conservation and with purely Lagrangian schemes with regard to interface resolution....
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...The L1 errors reported here compare favorably with those reported by Rider and Kothe in [28] using a VOF PLIC method....
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...To compare the fidelity of these schemes, Rider and Kothe proposed a set of test problems [27, 28] which approximate flows with large vortical components....
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...In a comparison of various Lagrangian and Eulerian methods for these flows, Rider and Kothe found that Lagrangian tracking schemes maintain filamentary interface structures better than their Eulerian counterparts....
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1,114 citations
968 citations
Cites background from "Reconstructing Volume Tracking"
...Many researchers have proposed techniques for this purpose and some alternatives are reviewed in [403, 404, 320]....
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947 citations
Cites methods from "Reconstructing Volume Tracking"
...This method is only first order accurate as shown in Table 1, where for completeness we present also the results from our implementation of a second-order least square algorithm for the normal estimation, as described in [ 15 , 16]....
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References
11,567 citations
"Reconstructing Volume Tracking" refers methods in this paper
...49 Rider and Kothe Reconstructing Volume Tracking LA{UR{96{2375[12] B. D. Nichols and C. W. Hirt....
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...5 Rider and Kothe Reconstructing Volume Tracking LA{UR{96{2375Author(s) Reconstructed Interface Geometry Time IntegrationDeBar [3] Piecewise Linear, Operator Split Operator SplitNoh and Woodward [4] Piecewise Constant, Operator Split Operator SplitHirt and Nichols [5] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator SplitChorin [6] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator SplitBarr and Ashurst [7] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator SplitAshgriz and Poo [8] Piecewise Linear, Operator Split Operator SplitYoungs [9] Piecewise Linear, Multi-Dimensional Operator SplitPilliod and Puckett [10, 11] Piecewise Linear, Multi-Dimensional Multi-DimensionalTable 1: Reconstructed interface geometry and time integration method used in a variety of pub-lished volume tracking algorithms.these methods chose a di erent reconstructed interface geometry: the DeBar algorithm used apiecewise linear approximation, the VOF method used a piecewise constant/"stair-stepped" ap-proximation, and the SLIC algorithm invoked a piecewise constant approximation....
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...[5] C. W. Hirt and B. D. Nichols....
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...[13] C. W. Hirt and B. D. Nichols....
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...Rider and Kothe Reconstructing Volume Tracking LA{UR{96{2375 Author(s) Reconstructed Interface Geometry Time Integration DeBar [3] Piecewise Linear, Operator Split Operator Split Noh and Woodward [4] Piecewise Constant, Operator Split Operator Split Hirt and Nichols [5] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator Split Chorin [6] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator Split Barr and Ashurst [7] Piecewise Constant, Stair-Stepped, Multi-Dimensional Operator Split Ashgriz and Poo [8] Piecewise Linear, Operator Split Operator Split Youngs [9] Piecewise Linear, Multi-Dimensional Operator Split Pilliod and Puckett [10, 11] Piecewise Linear, Multi-Dimensional Multi-Dimensional Table 1: Reconstructed interface geometry and time integration method used in a variety of published volume tracking algorithms....
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9,345 citations
4,148 citations
"Reconstructing Volume Tracking" refers methods in this paper
...The methods tested in [15] are those based on particles, level sets [42], and high resolution upwind schemes such as PPM [43]....
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3,892 citations
"Reconstructing Volume Tracking" refers methods in this paper
...The piecewise parabolic method (PPM) for gas-dynamical sim-ulations....
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...The methods tested in [15] are those based on particles, level sets [47], andstandard upwind continuum advection schemes such as fourth-order PPM [42].6 CONCLUSIONSA new second-order accurate method for the volume tracking of material interfaces in two dimen-sions has been presented....
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...The methods tested in [15] are those based on particles, level sets [47], and standard upwind continuum advection schemes such as fourth-order PPM [42]....
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...This time-centered velocity is given by ~ un+ 12 i+ 12 ;j = un+ 12 i+ 12 ;j 1 + 1 2 tux;i;j ; 2It is important to make a distinction between a Lagrangian-remap (LR) and direct-Eulerian (DE) formulation [41, 42]....
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3,556 citations