scholarly journals Solution of two-phase flow problems in porous media via an alternating-direction finite element method

1984 ◽  
Vol 8 (6) ◽  
pp. 391-396 ◽  
Author(s):  
K. Morgan ◽  
R.W. Lewis ◽  
P.M. Roberts
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Alternating Direction ◽  
Element Method

A parallel finite element method for two-phase flow processes in porous media: OpenGeoSys with PETSc

2014 ◽  
Vol 73 (5) ◽  
pp. 2269-2285 ◽  
Author(s):  
Wenqing Wang ◽  
Thomas Fischer ◽  
Björn Zehner ◽  
Norbert Böttcher ◽  
Uwe-Jens Görke ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Processes ◽  
Parallel Finite Element ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document