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 Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry
Yu-Heng Tseng,Joel H. Ferziger +1 more
TL;DR: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented in this paper, where a boundary condition is enforced through a ghost cell method.
Journal ArticleDOI
A ghost-cell immersed boundary method for flow in complex geometry
Yu-Heng Tseng,Joel H. Ferziger +1 more
TL;DR: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented in this article, where a boundary condition is enforced through a ghost cell method.
Journal ArticleDOI
An adaptive, formally second order accurate version of the immersed boundary method
TL;DR: The results obtaining by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution.
Journal ArticleDOI
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems
TL;DR: In this article, Lai et al. describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid-structure interaction problem, involving an immersed viscoelastic shell of finite thickness, studied over a broad range of Reynolds numbers.
Journal ArticleDOI
Solving pdes in complex geometries: a diffuse domain approach.
TL;DR: A general approach for solving partial differential equations in complex, stationary, or moving geometries with Dirichlet, Neumann, and Robin boundary conditions with matched asymptotic expansions is presented.
References
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Journal ArticleDOI
Second-order, L 0 -stable methods for the heat equation with time-dependent boundary conditions
TL;DR: A family of second-order,L0-stable methods is developed and analysed for the numerical solution of the simple heat equation with time-dependent boundary conditions and no oscillations are observed in the computed solutions.
Conservative front-tracking for inviscid compressible flow
TL;DR: A front-ncking algo-rithm for modeling the propagation of discontinuous waves in two space dimensions using a volume-of-fluid representation of the front in which the local frontal geometry is reconstructed from the state information on either side of the discontinuity and the Rankine·Hugoniot relations.
Journal Article
A higher-order embedded boundary method for time-dependent simulation of hyperbolic conservation laws
D. Modiano,Phillip Colella +1 more
TL;DR: A new method for time-dependent simulation of hyperbolic conservation laws using a background Cartesian grid with an embedded boundary to represent geometry, with consistent uxes, which converges at between rst and second order in the irregular cells, and at second orders in the full domain.
An embedded boundary method for the modeling of unsteady combustion in an industrial gas-fired furnace
R.B. Pember,Ann S. Almgren,W.Y. Crutchfield,Louis H. Howell,John B. Bell,Phillip Colella,V E Beckner +6 more
TL;DR: In this article, a new methodology for the modeling of non-premixed, axisymmetric reacting flow in industrial furnaces is presented, which is an extension of previous work by the authors to complex geometries, multistep kinetics mechanisms and realistic properties, especially thermochemical data.
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