Combination of direct-forcing fictitious domain method and sharp interface method for dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.

Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods

This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.

An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.Since the solution has low regularity across the interface,when applying finite difference discretization to this problem,an additional treatment accounting for the jump discontinuities must be employed.Here,we aim to elevate such an extra effort to ease our implementation by machine learning methodology.The key idea is to decompose the solution into singular and regular parts.The neural network learning machinery incorporating the given jump conditions finds the singular solution,while the standard five-point Laplacian discretization is used to obtain the regular solution with associated boundary conditions.Regardless of the interface geometry,these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation,making the hybrid method easy to implement and efficient.The two-and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives,and it is comparable with the traditional immersed interface method in the literature.As an application,we solve the Stokes equations with singular forces to demonstrate the robustness of the present method.

Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.