Numerical solution of the Hele-Shaw equations
Technical Report
·
OSTI ID:6321969
An algorithm is presented for approximating the motion of the interface between two immiscible fluids in a Hele-Shaw cell. The interface is represented by a set of volume fractions. We use the Simple Line Interface Calculation method along with the method of fractional steps to transport the interface. The equation of continuity leads to a Poisson equation for the pressure. The Poisson equation is discretized. Near the interface where the velocity field is discontinuous, the discretization is based on a weak formulation of the continuity equation. Interpolation is used on each side of the interface to increase the accuracy of the algorithm. The weak formulation as well as the interpolation are based on the computed volume fractions. This treatment of the interface is new. The discretized equations are solved by a modified conjugate gradient method. Surface tension is included and the curvature is computed through the use of osculating circles. For perturbations of small amplitude, a surprisingly good agreement is found between the numerical results and linearized perturbation theory. Numerical results are presented for the finite amplitude growth of unstable fingers. 62 refs., 13 figs.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6321969
- Report Number(s):
- LBL-23342; ON: DE87011211
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
CONTINUITY EQUATIONS
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLOW MODELS
FLUID FLOW
INCOMPRESSIBLE FLOW
INFORMATION
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NUMERICAL DATA
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POISSON EQUATION
THREE-DIMENSIONAL CALCULATIONS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
CONTINUITY EQUATIONS
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLOW MODELS
FLUID FLOW
INCOMPRESSIBLE FLOW
INFORMATION
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NUMERICAL DATA
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POISSON EQUATION
THREE-DIMENSIONAL CALCULATIONS