A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection sche
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Vol. 2, No. 4, 2020, 00–00 https:// doi.org/10.1007/s42757-020-0074-2
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 1. Institute of Numerical Methods in Mechanical Engineering (FNB), Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany 2. Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Abstract
Keywords
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
volume of fluid (VOF)
the numerical stability and convergence depend heavily on the numerical advection scheme and implementation method. The proposed method is based on the normalized weighting
discretization method
factor (NWF) method, which linearizes the normalized interpolation profile and rewrites the face
efficiency
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
Article History
weighting factor (MNWF) method only forms the implicit terms with the contribution of the
Received: 28 February 2020
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
Revised: 19 April 2020
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
Research Article
advection two-phase flow
Accepted: 25 April 2020
© The Author(s) 2020
be obtained with less computational time.
1
Introduction
The volume of fluid (VOF) method of Hirt and Nichols (1981) is a well-established conservative method to solve multiphase flow problems. The VOF introduces an additional transport equation to advent a marker function called volume fraction to define the position of the interface between the fluids. The volume fraction must be updated every time that the fluids move, and the boundary between the different fluids changes position. Nevertheless, updating the marker function is critical for the success of the simulation of multiphase flows and also is not a trivial job due to the purely convective nature of the transport equation (Tryggvason et al., 2001). An option to deal with this problem is using the blended High Resolution (HR) schemes also known as interface-capture schemes which combine a high order (HO) diffusive scheme, a compressive scheme, and the Convection [email protected]
Boundedness Criterion (CBC) ensuring that no oscillatory behavior is experienced in the solution and have relatively low numeric
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