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Full-Text Articles in Physical Sciences and Mathematics
Convergence Of The Boundary Integral Method For Interfacial Stokes Flow, Keyang Zhang
Convergence Of The Boundary Integral Method For Interfacial Stokes Flow, Keyang Zhang
Dissertations
Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no analysis of the convergence of these methods for interfacial Stokes flow. In practice, the stability of discretizations of the boundary integral formulation can depend sensitively on details of the discretization and on the application of numerical filters. A convergence analysis of the boundary integral method for Stokes flow …
Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater
Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater
Dissertations
Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity
In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this …