A non-stiff boundary integral method for 3D porous media flow with surface tension

2012 ◽  
Vol 82 (6) ◽  
pp. 968-983 ◽  
Author(s):  
David M. Ambrose ◽  
Michael Siegel
Keyword(s):  
Surface Tension ◽  
Porous Media ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Porous Media Flow

scholarly journals A boundary integral method for contaminant transport in two adjacent porous media

1989 ◽  
Vol 30 (3) ◽  
pp. 251-267 ◽  
Author(s):  
K. A. Landman
Keyword(s):  
Integral Equation ◽  
Porous Media ◽  
Contaminant Transport ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Contaminant Concentration ◽  
Two Dimensional ◽  
Initial Concentration ◽  
Media Systems

AbstractThe problem of transient two-dimensional transport by diffusion and advection of a decaying contaminant in two adjacent porous media is solved using a boundary-integral method. The method requires the construction of appropriate Green's functions. Application of Green's theorem in the plane then yields representations for the contaminant concentration in both regions in terms of an integral of the initial concentration over the region's interior and integrals along the boundaries of known quantities and the unknown interfacial flux between the two adjacent media. This flux is given by a first-kind integral equation, which can be solved numerically by a discretisation technique. Examples of contaminant transport in fractured porous media systems are presented.

Surface-tension effects in the contact of liquid surfaces

1989 ◽  
Vol 203 ◽  
pp. 149-171 ◽  
Author(s):  
Hasan N. Oguz ◽  
Andrea Prosperetti
Keyword(s):  
Surface Tension ◽  
Experimental Evidence ◽  
Integral Method ◽  
Model Problem ◽  
Mathematical Formulation ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Inviscid Fluid ◽  
Condensation Nuclei ◽  
Rain Drops

The process by which two surfaces of the same liquid establish contact, as when two drops collide or raindrops fall on water, is studied. The mathematical formulation is based on the assumption of an incompressible, inviscid fluid with surface tension. A model problem with a simplified geometry is solved numerically by means of a boundary-integral method. The results imply that a number of toroidal bubbles form and remain entrapped between the contacting surfaces. Experimental evidence for this process, which is important for boiling nucleation and the formation of condensation nuclei for rain drops, is found in the literature.

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