A mixed finite element method for Hele-Shaw cell equations |
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| Authors: | J M Guevara-Jordan J Glimm |
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| Institution: | (1) Facultad de Ciencias, Escuela de Física y Matemáticas, Universidad Central de Venezuela, Caracas, Venezuela |
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| Abstract: | A new numerical method to solve the system of equations describing two phase flow in a Hele-Shaw cell is presented. It combines
a mixed finite element method, the method of subtraction of the singularity and a front tracking grid in a single computational
strategy. This choice of discretization techniques is well motivated by the difficulties present in the system of equations
and the physics of the problem. The new method was tested against analytical solutions and also by solving the Saffman–Taylor
viscous fingering problem for finite and infinite mobility ratios. In both cases convergence under mesh refinement is achieved
for the fingers developed from an initial sinusoidal interface. Finger splitting is observed for low values of the surface
tension and high mobility ratio. Different explanations, based in our results, are provided for this phenomenon.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | front tracking interface mixed mobility ratio singularity surface tension 65C20 76T05 76S05 |
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