Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
A level set approach for computing solutions to incompressible two-phase flow
A level set approach for computing solutions to incompressible two-phase flow
Continuum-kinetic-microscopic model of lung clearance due to core-annular fluid entrainment
Journal of Computational Physics
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We simulate the axisymmetric pipeline transportation of oil and water numerically under the assumption that the densities of the two fluids are different and that the viscosity of the oil core is very large. We develop the appropriate equations for core-annular flows using the level set methodology. Our method consists of a finite difference scheme for solving the model equations, and a level set approach for capturing the interface between two liquids (oil and water). A variable density projection method combined with a TVD Runge---Kutta scheme is used to advance the computed solution in time. The simulations succeed in predicting the spatially periodic waves called bamboo waves, which have been observed in the experiments of [Bai et al. (1992) J. Fluid Mech. 240, 97---142.] on up-flow in vertical core flow. In contrast to the stable case, our simulations succeed in cases where the oil breaks up in the water, and then merging occurs. Comparisons are made with other numerical methods and with both theoretical and experimental results.