zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Reconstructing volume tracking. (English) Zbl 0933.76069
Summary: A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a well-defined, second-order geometric solution of a volume evolution equation. The method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology. A linearity-preserving, piecewise linear interface geometry approximation ensures that solutions generated retain second-order spatial accuracy. Second-order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme. We detail our geometrically based solution method, in which material volume fluxes are computed systematically with a set of simple geometric tasks. We then interrogate the method by testing its ability to track interfaces through large, controlled topology changes, whereby an initially simple interface configuration is subjected to vortical flows. Numerical results for these strenuous test problems provide evidence for the algorithm’s improved solution quality and accuracy. $\copyright$ Academic Press.

MSC:
76M25Other numerical methods (fluid mechanics)
76B47Vortex flows
Software:
CAVEAT; KRAKEN
WorldCat.org
Full Text: DOI
References:
[1] Strang, G.: On the construction and comparison of difference schemes. SIAM J. Numer. anal. 5, 506 (1968) · Zbl 0184.38503
[2] Zalesak, S. T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. comput. Phys. 31, 335 (1979) · Zbl 0416.76002
[3] Debar, R.: Fundamentals of the KRAKEN code. (1974)
[4] Noh, W. F.; Woodward, P. R.: SLIC (simple line interface method). Lecture notes in phys. 59, 330 (1976) · Zbl 0382.76084
[5] Hirt, C. W.; Nichols, B. D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. comput. Phys. 39, 201 (1981) · Zbl 0462.76020
[6] Chorin, A. J.: Flame advection and propagation algorithms. J. comput. Phys. 35, 1 (1980) · Zbl 0425.76086
[7] Barr, P. K.; Ashurst, W. T.: An interface scheme for turbulent flame propagation. (1984)
[8] Ashgriz, N.; Poo, J. Y.: FLAIR--flux line-segment model for advection and interface reconstruction. J. comput. Phys. 93, 449 (1991) · Zbl 0739.76012
[9] D. L. Youngs, Time-dependent multi-material flow with large fluid distortion, Numerical Methods for Fluid Dynamics, K. W. MortonM. J. Baines, Academic Press, New York, 1982, 273
[10] Jr., J. E. Pilliod: An analysis of piecewise linear interface reconstruction algorithms for volume-of-fluid methods. (1992)
[11] J. E. Pilloid Jr. E. G. Puckett, Second-order volume-of-fluid algorithms for tracking material interfaces, J. Comput. Phys.
[12] Nichols, B. D.; Hirt, C. W.: Methods for calculating multi-dimensional, transient free surface flows past bodies. (1975)
[13] Hirt, C. W.; Nichols, B. D.: A computational method for free surface hydrodynamics. Journal of pressure vessel technology 103, 136 (1981) · Zbl 0462.76020
[14] M. L. Norman, K.-H. A, Winkler, 2-D Eulerian hydrodynamics with fluid interfaces, Astrophysical Radiation Hydrodynamics, K.-H. A, WinklerM. L. Norman, 1986, 187
[15] Rider, W. J.; Kothe, D. B.: Stretching and tearing interface tracking methods. The 12th AIAA CFD conference (1995)
[16] Bowers, R. L.; Wilson, J. R.: Numerical modeling in applied physics and astrophysics. (1991) · Zbl 0786.76001
[17] R. L. Bowers
[18] Rudman, M.: Volume tracking methods for interfacial flow calculations. International journal for numerical methods in fluids 24, 671 (1997) · Zbl 0889.76069
[19] Boris, J. P.; Book, D. L.: Flux-corrected transport I. SHASTA, a fluid transport algorithm that works. J. comput. Phys. 11, 38 (1973) · Zbl 0251.76004
[20] Lafaurie, B.; Nardone, C.; Scardovelli, R.; Zaleski, S.; Zanetti, G.: Modelling merging and fragmentation in multiphase flows with SURFER. J. comput. Phys. 113, 134 (1994) · Zbl 0809.76064
[21] Youngs, D. L.: An interface tracking method for a 3D Eulerian hydrodynamics code. (1984)
[22] Addessio, F. L.; Carroll, D. E.; Dukowicz, J. K.; Harlow, F. H.; Johnson, J. N.; Kashiwa, B. A.; Maltrud, M. E.; Ruppel, H. M.: CAVEAT: A computer code for fluid dynamics problems with large distortion and internal slip. (1986)
[23] Holian, K. S.; Mosso, S. J.; Mandell, D. A.; Henninger, R.: MESA: A 3-D computer code for armor/anti-armor applications. (1991)
[24] Kothe, D. B.; Baumgardner, J. R.; Bennion, S. T.; Cerutti, J. H.; Daly, B. J.; Holian, K. S.; Kober, E. M.; Mosso, S. J.; Painter, J. W.; Smith, R. D.; Torrey, M. D.: PAGOSA: A massively-parallel, multi-material hydro-dynamics model for three-dimensional high-speed flow and high-rate deformation. (1992)
[25] Perry, J. S.; Budge, K. G.; Wong, M. K. W.; Trucano, T. G.: Rhale: A 3-D MMALE code for unstructured grids. Advanced computational methods for material modeling, AMD-vol. 180/PVP-vol. 268 180, 159 (1993)
[26] Puckett, E. G.: A volume of fluid interface tracking algorithm with applications to computing shock wave rarefraction. Proceedings, 4th international symposium on computational fluid dynamics, 933 (1991)
[27] P. Colella, L. F. Henderson, E. G. Puckett, A numerical study of shock wave refractions at a gas interface, Proceedings of the AIAA Ninth Computational Fluid Dynamics Conference, T. Pulliam, 1989, 426
[28] Puckett, E. G.; Saltzman, J. S.: A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics. Physica D 60, 84 (1992) · Zbl 0779.76059
[29] Berger, M. J.; Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. comput. Phys. 82, 64 (1989) · Zbl 0665.76070
[30] Bell, J.; Berger, M.; Saltzman, J. S.; Welcome, M.: Three dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM journal on scientific computing 15, 127 (1994) · Zbl 0793.65072
[31] S. J. Mosso, B. K. Swartz, D. B. Kothe, R. C. Ferrell, A parallel, volume tracking algorithm for unstructured meshes, Parallel Computational Fluid Dynamics ’96, Italy, 1996, P. Schiano
[32] Kothe, D. B.; Rider, W. J.; Mosso, S. J.; Brock, J. S.; Hochstein, J. I.: Volume tracking of interfaces having surface tension in two and three dimensions. (1996)
[33] Rider, W. J.; Kothe, D. B.; Mosso, S. J.; Cerruti, J. H.; Hochstein, J. I.: Accurate solution algorithms for incompressible multiphase fluid flows. (1995)
[34] W. J. Rider, D. B. Kothe, S. J. Mosso, J. H. Cerruti, J. I. Hochstein, Reno, NV, Jan 9--12 1995, http://www-xdiv.lanl.gov/XHM/personnel/wjr/Web_papers/pubs.html
[35] Kothe, D. B.: Et al.. (1995)
[36] Puckett, E. G.; Almgren, A. S.; Bell, J. B.; Marcus, D. L.; Rider, W. J.: A second-order projection method for tracking fluid interfaces in variable density incompressible flows. J. comput. Phys. 130, 269 (1997) · Zbl 0872.76065
[37] O’rourke, J.: Computational geometry in C. (1993)
[38] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P.: Numerical recipes in Fortran. (1986) · Zbl 0587.65005
[39] Bell, J. B.; Colella, P.; Glaz, H. M.: A second-order projection method of the incompressible Navier--Stokes equations. J. comput. Phys. 85, 257 (1989) · Zbl 0681.76030
[40] Dukowicz, J. K.: New methods for conservative rezoning (Remapping) for general quadrilateral meshes in rezoning workshop 1983. (1984) · Zbl 0534.76008
[41] Smolarkiewicz, P. K.: The multi-dimensional crowley advection scheme. Monthly weather review 110, 1968 (1982)
[42] Leveque, R. J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. anal. 33, 627 (1996) · Zbl 0852.76057
[43] Sussman, M.; Smereka, P.; Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. comput. Phys. 114, 146 (1994) · Zbl 0808.76077
[44] Colella, P.; Woodward, P.: The piecewise parabolic method (PPM) for gas-dynamical simulations. J. comput. Phys. 54, 174 (1984) · Zbl 0531.76082
[45] Barth, T. J.: Aspects of unstructured grids and finite-volume solvers for Euler and Navier--Stokes equations. (1995)
[46] Swartz, B.: The second-order sharpening of blurred smooth borders. Mathematics of computation 52, 675 (1989) · Zbl 0667.65005