Computing fluid-fluid interface evolution in Hele-Shaw cells using rational approximation

Abstract

We deploy a rational solver to compute moving boundary problems in Hele-Shaw cells and porous media. At each time, a quasi-stationary Laplace problem for the pressure is solved using rational approximation. This furnishes the interfacial velocity from which the moving boundary is updated. Two approaches for representing the moving boundary are presented: orthonormal basis functions (such as Chebyshev polynomials) and level-set functions. For fluid domains with corners that are stationary or translate in a simple fashion, poles are exponentially clustered exterior to the fluid domain in the vicinity of the corner and moved in step with the respective vertex. In the case of more complicated fl..