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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
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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

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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

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

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