Q1. What are the contributions mentioned in the paper "A cartesian grid embedded boundary method for the heat equation on irregular domains" ?
The authors present an algorithm for solving the heat equation on irregular time-dependent domains.
A Cartesian grid embedded boundary method for the heat equation on irregular domains
TLDR
An algorithm for solving the heat equation on irregular time-dependent domains is presented, based on the Cartesian grid embedded boundary algorithm of Johansen and Colella, combined with a second-order accurate discretization of the time derivative.About:
This article is published in Journal of Computational Physics.The article was published on 2001-11-13 and is currently open access. It has received 161 citations till now. The article focuses on the topics: Mixed boundary condition & Boundary (topology).read more
Figures
TABLE 3 
FIG. 6. Contour plots of absolute value of solution error to (19) at t = 1 for fixed boundaries, Dirichlet boundary conditions, h = 0:0125. Top figure is for Crank–Nicolson method, bottom figure for TGA method. 
FIG. 4. Solution error at t = 1 using Crank–Nicolson (stars) and TGA (circles), for the Dirichlet problem for (19) with fixed boundaries. Left-hand plot shows max norm, right-hand plot shows 1-norm. We see that both jj jj1 = O(h2) and jj jj1 = O(h2), indicating second-order accuracy. 
FIG. 5. Solution error at t = 1 using Crank–Nicolson (stars) and TGA (circles), for the Neumann problem for (19) with fixed boundaries. Left-hand plot shows max norm, right-hand plot shows 1-norm. We see that both jj jj1 = O(h2) and jj jj1 = O(h2), indicating second-order accuracy. 
FIG. 8. Contour plot of exact solution to (19) at t = 1 for moving-boundaryproblem. The dashed ellipses indicate the boundaries at t = 0. 
TABLE 1
Citations
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A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries
David Trebotich,Gregory H. Miller,Phillip Colella,Daniel Graves,Daniel F. Martin,P. O. Schwartz +5 more
TL;DR: In this paper, a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry is presented, which combines a ball-rod model representation for polymers coupled tightly with a projection method for incompressible viscous flow.
Proceedings ArticleDOI
Fictitious domain methods to solve convection-diffusion problems with general boundary conditions
TL;DR: The aim of this paper is to solve convection-diffusion problems with fictitious domain methods which can easily simulate free-boundary with possibly deformations of the boundary without increasing the computational cost.
Journal ArticleDOI
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
TL;DR: A scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries based on embedded boundary finite volume discretizations of the minimal fluid-plasma model on adaptive Cartesian grids is reviewed.
Journal ArticleDOI
A three-dimensional Cartesian cut-cell/volume-of-fluid method for two-phase flows with moving bodies
Zhihua Xie,Thorsten Stoesser +1 more
TL;DR: The versatility and robustness of the present two-phase flow model is illustrated via various two- and three-dimensional flow problems with fixed/moving bodies, such as dambreak flows with and without a square cylinder, a moving cylinder in a quiescent fluid, dambreak flow over a wet bed with a moving gate, water entry and exist of a circular cylinder, and landside-generated waves.
Journal ArticleDOI
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
Jeffrey K. Wiens,John M. Stockie +1 more
TL;DR: An efficient algorithm for the immersed boundary method on distributed-memory architectures that has the computational complexity of a completely explicit method and also has excellent parallel scaling is proposed.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book ChapterDOI
Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
Journal ArticleDOI
A second-order projection method for the incompressible navier-stokes equations
TL;DR: In this paper, a second-order projection method for the Navier-Stokes equations is proposed, which uses a specialized higher-order Godunov method for differencing the nonlinear convective terms.
Journal ArticleDOI
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
Hans Johansen,Phillip Colella +1 more
TL;DR: A numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions using a finite-volume discretization, which embeds the domain in a regular Cartesian grid.
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