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A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier–Stokes–Korteweg equations

Article dans une revue avec comité de lecture
Author
MARTÍNEZ, Abel
318580 University of A Coruña [UDC]
RAMÍREZ, Luis
318580 University of A Coruña [UDC]
NOGUEIRA, Xesús
318580 University of A Coruña [UDC]
ccKHELLADI, Sofiane
134975 Laboratoire de Dynamique des Fluides [DynFluid]
NAVARRINA, Fermín
318580 University of A Coruña [UDC]

URI
http://hdl.handle.net/10985/18007
DOI
10.1016/j.camwa.2019.07.021
Date
2020
Journal
Computers & Mathematics with Applications

Abstract

In this work we solve the Navier–Stokes–Korteweg (NSK) equations to simulate a two-phase fluid with phase change. We use these equations on a diffuse interface approach, where the properties of the fluid vary continuously across the interface that separates the different phases. The model is able to describe the behavior of both phases with the same set of equations, and it is also able to handle problems with great changes in the topology of the problem. However, high-order derivatives are present in NSK equations, which is a difficulty for the design of a numerical method to solve the problem. Here, we propose the use of a high-order Finite Volume method with Moving Least Squares approximations to handle high-order derivatives and solve the NSK equations. Moreover, a new methodology to obtain accurate equations of state is presented. In this method, we use any accurate equation of state for the pure phases. Under the saturation curve, a B-spline reconstruction fulfilling a given set of thermodynamic criteria is performed. The new EOS can be used for computations using diffuse interface modeling. Several numerical examples to show the accuracy of the new approach are presented.

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