Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
A numerical method for solving variable coefficient elliptic equation with interfaces
Journal of Computational Physics
Journal of Computational Physics
A second-order method for three-dimensional particle simulation
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
A direct-forcing fictitious domain method for particulate flows
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A Brinkman penalization method for compressible flows in complex geometries
Journal of Computational Physics
A fixed-mesh method for incompressible flow-structure systems with finite solid deformations
Journal of Computational Physics
DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
Prosperetti's seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest.