Solving partial differential equations on irregular domains with moving interfaces, with applications to superconformal electrodeposition in semiconductor manufacturing
We present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces. Instead of the typical approach of solving in a larger rectangular domain, our approach performs most calculations only in the ...
Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Fevrier et al. [P. Fevrier, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially ...
A grid-alignment finite element technique for incompressible multicomponent flows
We present a numerical method for solving the multicomponent incompressible Navier-Stokes equations. The methods employs a moving grid technique and a projection scheme based on low-order Crouzeix-Raviart and P"1 finite elements. The computational grid ...
Adjoint-based optimization of PDE systems with alternative gradients
In this work we investigate a technique for accelerating convergence of adjoint-based optimization of PDE systems based on a nonlinear change of variables in the control space. This change of variables is accomplished in the ''differentiate - then - ...
Prediction of cavitating flow noise by direct numerical simulation
In this study, a direct numerical simulation procedure for the cavitating flow noise is presented. The compressible Navier-Stokes equations are written for the two-phase fluid, employing a density-based homogeneous equilibrium model with a linearly-...
A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations
A new concept called the dominance of equidistribution is introduced for analyzing moving mesh partial differential equations for numerical simulation of blowup in reaction diffusion equations. Theoretical and numerical results show that a moving mesh ...
Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs
Non-equilibrium Green's function (NEGF) is a general method for modeling non-equilibrium quantum transport in open mesoscopic systems with many body scattering effects. In this paper, we present a unified treatment of quantum device boundaries in the ...
Numerical simulation of filamentary discharges with parallel adaptive mesh refinement
Direct simulation of filamentary gas discharges like streamers or dielectric barrier micro-discharges requires the use of an adaptive mesh. The objective of this paper is to develop a strategy which can use a set of grids with suitable local refinements ...
A convergence rate theorem for finite difference approximations to delta functions
We prove a rate of convergence theorem for approximations to certain integrals over codimension one manifolds in R^n. The type of manifold involved here is defined by the zero level set of a smooth mapping u:R^n@?R. Our approximations are based on the ...
Scaling the fractional advective-dispersive equation for numerical evaluation of microbial dynamics in confined geometries with sticky boundaries
Microbial motility is often characterized by 'run and tumble' behavior which consists of bacteria making sequences of runs followed by tumbles (random changes in direction). As a superset of Brownian motion, Levy motion seems to describe such a motility ...
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper ...
Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration
For the 1-dim. linear advection problem stability limits of Runge-Kutta (RK) methods from 1st to 7th order in combination with upwind or centered difference schemes from 1st to 6th order are presented. The analysis can be carried out in a rather general ...
Derivation and validation of a novel implicit second-order accurate immersed boundary method
A novel implicit second-order accurate immersed boundary method (IBM) for simulating the flow around arbitrary stationary bodies is developed, implemented and validated in this paper. The IBM is used to efficiently take into account the existence of ...
Fast numerical method for the Boltzmann equation on non-uniform grids
We introduce a new fast numerical method for computing discontinuous solutions to the Boltzmann equation and illustrate it by numerical examples. A combination of adaptive grids for approximation of the distribution function and an approximate fast ...
A Lagrangian, stochastic modeling framework for multi-phase flow in porous media
Many of the complex physical processes relevant for compositional multi-phase flow in porous media are well understood at the pore-scale level. In order to study CO"2 storage in sub-surface formations, however, it is not feasible to perform simulations ...