Numerical simulation of two-phase flow in porous media based on mimetic Green element method

2019 ◽  
Vol 101 ◽  
pp. 113-120
Author(s):  
Xiang Rao ◽  
Linsong Cheng ◽  
Renyi Cao ◽  
Weili Song ◽  
Xulin Du ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Green Element Method ◽  
Element Method

A finite element method for degenerate two-phase flow in porous media. Part II: Convergence

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vivette Girault ◽  
Beatrice Riviere ◽  
Loic Cappanera
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Almost Everywhere ◽  
Phase Saturation ◽  
Element Method

Abstract Convergence of a finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary unknowns. Well-posedness is obtained in [7]. Theoretical convergence is proved via a compactness argument. The numerical phase saturation converges strongly to a weak solution in L 2 in space and in time whereas the numerical phase pressures converge strongly to weak solutions in L 2 in space almost everywhere in time. The proof is not straightforward because of the degeneracy of the phase mobilities and the unboundedness of the derivative of the capillary pressure.

A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vivette Girault ◽  
Beatrice Riviere ◽  
Loic Cappanera
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Two Phase Flow ◽  
Flow Problem ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Existence Of A Solution ◽  
Element Method

Abstract A finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary unknowns. The discrete saturation satisfies a maximum principle. Stability of the scheme and existence of a solution are established.

A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media

2007 ◽  
Vol 300 (1-2) ◽  
pp. 35-49 ◽  
Author(s):  
Andreas G. Yiotis ◽  
John Psihogios ◽  
Michael E. Kainourgiakis ◽  
Aggelos Papaioannou ◽  
Athanassios K. Stubos
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Viscous Coupling ◽  
Coupling Effects ◽  
Two Phase
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