AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Experimental and Computational Multiphase Flow Article
PDF (5.2 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows

Jessica Mariño-Salguero1,2( ), Michael Schäfer1,2
Institute of Numerical Methods in Mechanical Engineering (FNB), Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Show Author Information

Abstract

This work deals with a new methodology for the implementation of high-resolution (HR) schemes employed to advect the volume fraction in the volume of fluid (VOF) method, in which the numerical stability and convergence depend heavily on the numerical advection scheme and implementation method. The proposed method is based on the normalized weighting factor (NWF) method, which linearizes the normalized interpolation profile and rewrites the face value directly using the donor, acceptor, and upwind nodes. However, unlike the NWF, which is fully implicit and results in pentadiagonal linear systems, the new modified normalized weighting factor (MNWF) method only forms the implicit terms with the contribution of the donor and acceptor nodes, while the contribution of the upwind node explicitly forms part of the source term. Therefore, the method results in a tridiagonal linear system. The comparison of the new method with the deferred correction (DC), downwind weighting factor (DWF), and the RNWF methods shows that the MNWF requires about 5%-25% fewer iterations than DC and RNWF, and around 10%-85% less than DWF. Thus, a similar order of accuracy of the results can be obtained with less computational time.

Keywords

volume of fluid (VOF)advectiondiscretization methodtwo-phase flowefficiency

References

 
T. Chourushi, 2018. Computationally inexpensive and revised normalized weighting factor method for segregated solvers. Int J Comput Math, 95: 1622-1653.
Google Scholar
 
M. S. Darwish,, F. Moukalled, 1996. The normalized weighting factor method: A novel technique for accelerating the convergence of high-resolution convective schemes. Numer Heat Tr B: Fund, 30: 217-237.
Google Scholar
 
M. Darwish,, F. Moukalled, 2006. Convective schemes for capturing interfaces of free-surface flows on unstructured grids. Numer Heat Tr B: Fund, 49: 19-42.
Google Scholar
 
J. H. Ferziger,, M. Perić, 2012. Computational Methods for Fluid Dynamics, 3rd edn. Springer-Verlag Berlin Heidelberg.
 
P. H. Gaskell,, A. K. C. Lau, 1988. Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Int J Numer Meth Fl, 8: 617-641.
Google Scholar
 
C. W. Hirt,, B. D. Nichols, 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Physs, 39: 201-225.
Google Scholar
 
P. W. Hogg,, X. J. Gu,, D. R. Emerson, 2006. An implicit algorithm for capturing sharp fluid interfaces in the volume of fluid advection method. In: Proceedings of the European Conference on Computational Fluid Dynamics.
 
S. Hysing,, S. Turek,, D. Kuzmin,, N. Parolini,, E. Burman,, S. Ganesan,, L. Tobiska, 2009. Quantitative benchmark computations of two-dimensional bubble dynamics. Int J Numer Meth Fl, 60: 1259-1288.
Google Scholar
 
S. Koshizuka, 1995. A particle method for incompressible viscous flow with fluid fragmentation. Comput Fluid Dyn J, 4(29).
Google Scholar
 
B. P. Leonard, 1991. The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput Method Appl M, 88: 17-74.
Google Scholar
 
B. P. Leonard,, S. Mokhtari, 1990. Beyond first-order upwinding: The ultra-sharp alternative for non-oscillatory steady-state simulation of convection. Int J Numer Meth Eng, 30: 729-766.
Google Scholar
 
M. Malik,, E. S. C. Fan,, M. Bussmann, 2007. Adaptive VOF with curvature-based refinement. Int J Numer Meth Fl, 55: 693-712.
Google Scholar
 
J. Meyer,, H. Renzsch,, K. Graf,, T. Slawing, 2016. Advanced CDF-simulations of free-surface flows around modern sailing yachts using a newly developed OpenFOAM solver. In: Proceedings of the 22nd Chesapeake Sailing Yacht Symposium.
 
F. Moukalled,, L. Mangani,, M. Darwish, 2016. The Finite Volume Method in Computational Fluid Dynamics. Springer International Publishing Switzerland.
 
S. Muzaferija,, M. Perić,, P. C. Sames,, T. Shellin, 1998. A two-fluid Navier-Stokes solver to simulate water entry. In: Proceedings of the 22nd Symposium on Naval Hydrodynamics, 638-651.
 
J. K. Patel,, G. Natarajan, 2015. A generic framework for design of interface capturing schemes for multi-fluid flows. Comput Fluids, 106: 108-118.
Google Scholar
 
S. G. Rubin,, P. K. Khosla, 1977. Polynomial interpolation methods for viscous flow calculations. J Comput Phys, 24: 217-244.
Google Scholar
 
M. Rudman, 1997. Volume-tracking methods for interfacial flow calculations. Int J Numer Meth Fl, 24: 671-691.
Google Scholar
 
J. Sauer, 2000. Instationär kavitierende Strömungen: ein neues Modell, basierend auf front capturing (VoF) und Blasendynamik. Universität Karlsruhe.
 
G. Tryggvason,, R. Scardovelli,, S. Zaleski, 2001. Direct Numerical Simulations of Gas-Liquid Multiphase Flows. Cambridge University Press.
 
Y. Y. Tsui,, S. Lin,, T. Cheng,, T. C. Wu, 2009. Flux-blending schemes for interface capture in two-fluid flows. Int J Heat Mass Tran, 52: 5547-5556.
Google Scholar
 
S. Turek,, O. Mierka,, K. Bäumler, 2019. Numerical benchmarking for 3D multiphase flow: New results for a rising bubble. In: Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, Vol. 126. F. Radu,, K. Kumar,, I. Berre,, J. Nordbotten,, I. Pop, Eds. Springer Cham, 593-601.
 
O. Ubbink, 1997. Numerical prediction of two fluid systems with sharp interfaces. Imperial College of Science, Technology & Medicine, London, UK.
 
O. Ubbink,, R. I. Issa, 1999. A method for capturing sharp fluid interfaces on arbitrary meshes. J Comput Phys, 153: 26-50.
Google Scholar
 
J. Wackers,, B. Koren,, H. C. Raven,, A. van der Ploeg,, A. R. Starke,, G. B. Deng,, P. Queutey,, M. Visonneau,, T. Hino,, K. Ohashi, 2011. Free-surface viscous flow solution methods for ship hydrodynamics. Arch Comput Method E, 18: 1-41.
Google Scholar
 
T. Wacławczyk,, Ö. Caner Gemici,, M. Schäfer, 2007. Novel high- resolution scheme for interface capturing in multi-phase flow. In: Proceedings of the 6th International Conference on Multiphase Flow, S1-Fri-A64.
 
S. T. Zalesak, 1979. Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys, 31: 335-362.
Google Scholar
 
D. Zhang,, C. Jiang,, D. Liang,, Z. Chen,, Y. Yang,, Y. Shi, 2014. A refined volume-of-fluid algorithm for capturing sharp fluid interfaces on arbitrary meshes. J Comput Phys, 274: 709-736.
Google Scholar
Experimental and Computational Multiphase Flow
Volume 3 Issue 3,
September 2021
Pages 208-225
DOI: 10.1007/s42757-020-0074-2
Cite this article:
Mariño-Salguero J, Schäfer M. A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows. Experimental and Computational Multiphase Flow, 2021, 3(3): 208-225. https://doi.org/10.1007/s42757-020-0074-2

834

Views

20

Downloads

5

Crossref

7

Web of Science

6

Scopus

Altmetrics
Received: 28 February 2020
Revised: 19 April 2020
Accepted: 25 April 2020
Published: 18 July 2020
© The Author(s) 2020

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Return