MLPG_R method for modelling 2D flows of two immiscible fluids



Zhou, Yan ORCID: 0000-0001-6867-6275, Ma, QW and Yan, S
(2017) MLPG_R method for modelling 2D flows of two immiscible fluids. International Journal for Numerical Methods in Fluids, 84 (7). 385 - 408.

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Abstract

This is a first attempt to develop the Meshless Local Petrov–Galerkin method with Rankine source solution (MLPG_R method) to simulate multiphase flows. In this paper, we do not only further develop the MLPG_R method to model two‐phase flows but also propose two new techniques to tackle the associated challenges. The first technique is to form an equation for pressure on the explicitly identified interface between different phases by considering the continuity of the pressure and the discontinuity of the pressure gradient (i.e. the ratio of pressure gradient to fluid density), the latter reflecting the fact that the normal velocity is continuous across the interface. The second technique is about solving the algebraic equation for pressure, which gives reasonable solution not only for the cases with low density ratio but also for the cases with very high density ratio, such as more than 1000. The numerical tests show that the results of the newly developed two‐phase MLPG_R method agree well with analytical solutions and experimental data in the cases studied. The numerical results also demonstrate that the newly developed method has a second‐order convergent rate in the cases for sloshing motion with small amplitudes

Item Type: Article
Uncontrolled Keywords: meshless method, multiphase flow, high density ratio, MLPG_R method, sloshing
Depositing User: Symplectic Admin
Date Deposited: 06 Mar 2017 08:34
Last Modified: 12 Oct 2021 13:10
DOI: 10.1002/fld.4353
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3006204