A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
Hans Johansen,Phillip Colella +1 more
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TLDR
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.About:
This article is published in Journal of Computational Physics.The article was published on 1998-11-01 and is currently open access. It has received 470 citations till now. The article focuses on the topics: Mixed boundary condition & Adaptive mesh refinement.read more
Citations
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Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
TL;DR: An adaptive mesh projection method for the time-dependent incompressible Euler equations is presented and second-order convergence in space and time is demonstrated on regular, statically and dynamically refined grids.
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.
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A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains
TL;DR: The Ghost Fluid Method (GFM) as discussed by the authors was developed to capture the boundary conditions at a contact discontinuity in the inviscid Euler equations and has been extended to treat more general discontinuities such as shocks, detonations, and deflagrations and compressible viscous flows.
Journal ArticleDOI
A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies
TL;DR: In this paper, a numerical method is developed for solving the Navier-Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics.
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.
Journal ArticleDOI
Local adaptive mesh refinement for shock hydrodynamics
Marsha Berger,Phillip Colella +1 more
TL;DR: An automatic, adaptive mesh refinement strategy for solving hyperbolic conservation laws in two dimensions and how to organize the algorithm to minimize memory and CPU overhead is developed.
Book
A multigrid tutorial
TL;DR: This paper presents an implementation of Multilevel adaptive methods for Algebraic multigrid (AMG), a version of which has already been described in more detail in the preface.
Book
Adaptive mesh refinement for hyperbolic partial differential equations
Marsha Berger,Joseph Oliger +1 more
TL;DR: This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.
Book
Numerical Solution of Partial Differential Equations by the Finite Element Method
TL;DR: In this article, the authors present an easily accessible introduction to one of the most important methods used to solve partial differential equations, which they call finite element methods for integral equations (FEME).
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