The use of the one-fluid formulation to regularize the discontinuity of the fluid flow properties in multiphase flow solvers is widely extended in the computational flow community. This approach consists in replacing an infinitely thin interface by a diffuse interface region where an artificial volume fraction of the mixture is defined across a relatively thin region with a characteristic length varying from one cell to several grid sizes depending on the formulation used to represent the interface (Volume of Fluid, Level Set, etc...). Based on this artificial mixture region, the effective fluid properties quickly transit between the values of the properties of the two phases. In this work we will discuss the errors associated to this numerical model in the context of heat transfer equation by comparing the analytical solutions obtained for a sharp interface with that of a diffused interface of given thickness. The results will be then compared with those obtained numerically with a standard discretization of the heat flow equation available in Basilisk. In the final part of the talk, we will discuss the direct implications of the conclusions extracted for the heat transfer problem for the solution of the Navier-Stokes equations using the  effective one-fluid formulation. The results of this study provide new insights about the impact of the regularization on the jump of flow properties on the results, which can have direct application in the design of effective mesh refinement strategies or the development of high order methods using the one-fluid formulation.  

 

Daniel Fuster is Directeur de Recherche CNRS at the D’ Alembert Institute at Sorbonne Université in Paris. He received his PhD in Fluid Mechanics in 2007 from Universidad de Zaragoza (Spain). After two postdoctoral stays at the D’ Alembert Institute (Paris) and the Computational Flow Physics group at Caltech (USA), he obtains a CNRS research position as a permanent researcher (Chargé de Recherche) at D’ Alembert in 2010. His research career is focused on the development of numerical techniques for the solution of the full Navier-- Stokes equations for both incompressible and compressible multiphase flows, contributing to the development of free softwares such as Basilisk, Gerris or PARIS Simulator. In particular he is interested in conservative schemes at the discrete level and adaptive mesh refinement techniques applied to multiphase flow problems. In addition, he is also interested in the use of numerical techniques to improve the physical understanding of challenging multiphase flow problems, including the development of numerical models for the response of bubbles to external pressure changes for problems related to cavitation and wave propagation in bubbly flows, as well as investigations on diverse aspects of atomization/fragmentation processes.

 

Professor Fuster website can be found under this link