Numerical Schemes for Modelling Two Phase Flow with Interfaces

Jozef Minár

doi:10.4028/www.scientific.net/DDF.365.1

Paper Titles

Preface and Committees

Numerical Schemes for Modelling Two Phase Flow with Interfaces
p.1

Diffusion Induced Changes in Eutectic Carbides in Wrought M2 High-Speed Steel at Austenitising
p.5

Analysis of Freeze-Drying and Rehydration of Açai (Euterpe oleracea Martius)
p.11

Dynamic Analysis of Delaminated Beams
p.17

The Stability of CeNi₃-Based Intermetallic Hydrides
p.24

The Effect of Heat Treatment on Morphology and Phase Composition of Grain Boundary Phases in Mg-Zn-Y-Nd-Zr
p.30

Hydrogen Trapping at Defects in Pd and Thermally Activated Desorption
p.36

Influence of Natural Ageing on Precipitation Processes during Isochronal Annealing in MgGd Alloys
p.42

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Numerical Schemes for Modelling Two Phase Flow with Interfaces

Abstract:

We discuss the numerical modelling of two phase flow in porous media (see [1]). We consider a one-dimensional problem describing flow of two incompressible and immiscible fluids through a porous medium where the non-wetting phase (oil) is displaced by the wetting fluid (water). The used model is based on Darcy’s law and we consider either horizontal (neglecting the influence of gravity) or vertical flow. In case of horizontal flow, we compare our solution with analytical solution published in [2]. In case of gravity driven vertical flow, there is no known analytical solution and we propose our solution as a benchmark solution.Our numerical model is based on the modelling of interface separating zones where the water is present and where it is not. We semidiscretize the problem in space and obtain a mass preserving system of ODEs. We have moving grid points only on region where the water is present, and these move accordingly to the evolution of the interface. We can choose to have non-equidistant grid with more grid points in the neighbourhood of the interface. This guarantees very good approximation of sharp fronts during infiltration. Results obtained by our methods are compared with well-known result in [2] which was obtained by semi-analytical method and they are in perfect agreement.