Numerical methods for initial value problems in ordinary differential equations
Numerical methods for initial value problems in ordinary differential equations
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
A multipole-accelerated algorithm for close interaction of slightly deformable drops
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational Physics
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
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Since the pioneering work of Youngren and Acrivos [G.K. Youngren, A. Acrivos, On the shape of a gas bubble in a viscous extensional flow, J. Fluid Mech. 76 (1976) 433-442] 30 years ago, interfacial dynamics in Stokes flow has been implemented through explicit time integration of boundary integral schemes which require that the time step is sufficiently small to ensure numerical stability. To avoid this difficulty, we have developed an efficient, fully-implicit time-integration algorithm based on a mathematically rigorous combination of implicit formulas with a Jacobian-free three-dimensional Newton method. The resulting algorithm preserves the stability of the employed implicit formula and thus it has strong stability properties, e.g. it is not affected by the Courant condition or by physical stiffness such as that associated with the critical conditions of interfacial deformation. In our work, the numerical solution of our implicit algorithm is achieved through our spectral boundary element method. Our numerical results for free-suspended droplets are in excellent agreement with experimental findings, analytical predictions and earlier computational results at both subcritical and supercritical conditions, and establish the properties of our fully-implicit spectral boundary element algorithm.