A Eulerian level set/vortex sheet method for two-phase interface dynamics
Journal of Computational Physics
A boundary integral formulation of quasi-steady fluid wetting
Journal of Computational Physics
Short note: Moore's law and the Saffman-Taylor instability
Journal of Computational Physics
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
High order quadratures for the evaluation of interfacial velocities in axi-symmetric Stokes flows
Journal of Computational Physics
Efficient numerical methods for multiple surfactant-coated bubbles in a two-dimensional stokes flow
Journal of Computational Physics
Journal of Computational Physics
A Higher Order Scheme for a Tangentially Stabilized Plane Curve Shortening Flow with a Driving Force
SIAM Journal on Scientific Computing
Journal of Computational Physics
A non-stiff boundary integral method for 3D porous media flow with surface tension
Mathematics and Computers in Simulation
Spatial and temporal stability issues for interfacial flows with surface tension
Mathematical and Computer Modelling: An International Journal
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
The Explicit-Implicit-Null method: Removing the numerical instability of PDEs
Journal of Computational Physics
Hi-index | 31.52 |
A new formulation and new methods are presented for computing the motion of fluid interfaces with surface tension in two-dimensional, irrotational, and incompressible fluids. Through the Laplace-Young condition at the interface, surface tension introduces high-order terms, both nonlinear and nonlocal, into the dynamics. This leads to severe stability constraints for explicit time integration methods and makes the application of implicit methods difficult. This new formulation has all the nice properties for time integration methods that are associated with having a linear, constant coefficient, highest order term. That is, using this formulation, we give implicit time integration methods that have no high order time step stability constraint associated with surface tension and are explicit in Fourier space. The approach is based on a boundary integral formulation and applies more generally, even to problems beyond the fluid mechanical context. Here they are applied to computing with high resolution the motion of interfaces in Hele-Shaw flows and the motion of free surfaces in inviscid flows governed by the Euler equations. One Hele-Shaw computation shows the behavior of an expanding gas bubble over long-time as the interface undergoes successive tip-splittings and finger competition. A second computation shows the formation of a very ramified interface through the interaction of surface tension with an unstable density stratification. In Euler flows, the computation of a vortex sheet shows its roll-up through the Kelvin-Helmholtz instability. This motion culminates in the late time self-intersection of the interface, creating trapped bubbles of fluid. This is, we believe, a type of singularity formation previously unobserved for such flows in 2D. Finally, computations of falling plumes in an unstably stratified Boussinesq fluid show a very similar behavior.