PIC has been successfully used for plasma simulation in
the last two decades. The extension of PIC with AMR has
been explored recently, however, with the observation of
large self-force on the particles around the refinement
interface. Although the approach to control the
self-force is proposed for one-particle model, robust
choices of numerical parameters and numerical tests for
many-particle model haven't been addressed. Our starting
point for addressing those questions is the solving of
Poisson equation with infinite domain condition, since
we currently concentrate on electrostatic PIC model.
The dynamics of a continuum fluid with discrete embedded
polymers is important for certain microfluidic
applications,(e.g., so-called lab-on-a-chip PCR
reactors)and for modeling viscoelastic phenomena in the
dilute limit. Toward this end we proposed a
fluid-particle coupling strategy that uses Brownian
dynamics to approximate molecular-level fluid--polymer
interactions. To simulate polymer flows in microscale
environments we have developed a numerical method that
couples stochastic particle dynamics with an efficient
incompressible Navier-Stokes solver. Here, we examine
the convergence properties of the stochastic particle
solver alone, and demonstrate that it has second order
convergence in both weak and strong senses, for the
examples presented. In this work we consider the
framework of a freely-jointed chain (no polymer-polymer
interactions)and the fluid velocity field to be prescribed.
The microstructural evolution and kinetics of thermal and strain-induced
grain growth were analyzed using a two dimensional Monte Carlo Potts
(MCP) model. MCP simulations have captured various grain growth
behaviors; however, the stochastic nature of the MCP time-step limits its
verification with physical data. An energy-controlled relationship between
MCP and physical time-steps was established using thermal grain growth
simulations and published experimental data. The case of static strain-
induced growth is considered next. An internal energy term is introduced to
model the elastic stresses caused by the strain-induced dislocations in the
microstructure. The modeling strategies for the strain-induced energy,
recovery and nucleation and their implementations are discussed in
connection with experimental evidence.
We employ Jame-Lackner's boundary potential method for
infinite Poisson problem. In this method, the infinite
Poisson problem is represented by a Poisson problem with
appropriate Dirichlet boundary condition. The Dirichlet
boundary values can be found by solving two Dirichlet
problems, plus a boundary-to-boundary convolution. For
efficiency, we implement this by solving one of the
Dirichlet problems with fast multigrid-based Poisson
solver and another one with fast Fouries transformation.
The boundary-to-boundary convolution is calculated using
fast multipole method. The code has been developed based
on Chombo library, a software package applying finite
difference methods for the solution of partial
differential equations on a hierarchy of locally refined
grids. We compare the exact solution with the computed
solution in both 2D and 3D test cases. Second order
accuracy in L1 has been demonstrated in the tests.
With the infinite domain Poisson problem successfully
solved on a hierarchy of refined grids, our next step
will be coupling particle properties with grid ones.
This includes depositing the charge defined on particles
to grids and interpolating the force calculated on the
grids back to the particles. Carefully approach will be
used to control the self-force on the particles located
in the neighborhood of coarse-fine interface. After
rigorously analyzing the errors and running a bunch of
numerical tests, the mechanism of choosing robust
parameters will be developed. At last, the algorithms
will be used for simulating real beam problem and
verified through experiment results.
A Higher Order Approach to Fluid-Particle Coupling in Microscale Polymer Flows
Bakytzhan Kallemov, Greg Miller, D.Trebotich
Towards Single Crystals Using Strain Induced Grain Growth
Corentin Guebels, Tien Tran, Ben Fell, Joanna Groza