Abstract
In this work we study two-phase flow with gravity either in 1-rock homogeneous media or 2-rocks composed media, this phenomenon can be modeled by a non-linear scalar conservation law with continuous flux function or discontinuous flux function, respectively. Our study is essentially from a numerical point of view, we apply the new Lagrangian-Eulerian finite difference method developed by Abreu and Pérez and the Lax-Friedrichs classic method to obtain numerical entropic solutions. Comparisons between numerical and analytical solutions show the efficiency of the methods even for discontinuous flux function.
Highlights
Many problems in engineering, physics and other areas of sciences lead us to the study of conservation laws
They model many physical phenomena that appear in aerodynamics, fluid mechanics, traffic flow, groundwater flow, multi-phase flow in porous media and others [7, 8, 9, 16, 19, 20, 26, 29, 30, 32]
Often there is more than one weak solution to the conservation law 1.1 with the same initial data, only one of them is physically correct, the so called entropic solution
Summary
Physics and other areas of sciences lead us to the study of conservation laws. They model many physical phenomena that appear in aerodynamics, fluid mechanics, traffic flow, groundwater flow, multi-phase flow in porous media and others [7, 8, 9, 16, 19, 20, 26, 29, 30, 32]. In general a scalar conservation law in one dimension takes the form: ut + ( f (u))x = 0,. Where u is the conserved quantity and f (u) is the flux function
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
