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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2-3/2013

01.02.2013

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

verfasst von: Frédéric Gibou, Chohong Min, Ron Fedkiw

Erschienen in: Journal of Scientific Computing | Ausgabe 2-3/2013

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Abstract

We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain’s boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain’s boundary and (iii) a quadtree/octree node-based adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.
Vorheriger Artikel An Efficient Algorithm for ℓ 0 Minimization in Wavelet Frame Based Image Restoration
Nächster Artikel Simulations of Supersonic Astrophysical Jets and Their Environments Using Level Set Methods

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Fußnoten
1
For stiff problems, one may prefer the first-order accurate implicit Euler method.
 
2
One may prefer a Newton’s form for constructing the interpolant \(\tilde{u}(x)\).
 
3
We use a time step of Δt=Δx 3/2 and Δt=Δx 2 to emulate a third- and a fourth-order scheme in time.
 
4
The tangential component of a velocity field changes a curve’s parameterization (if any), not its location.
 
5
In practice a third-order accurate scheme in time should be chosen.
 
6
The definition of the velocity does not depend on ϕ.
 
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Metadaten
Titel
High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries
verfasst von
Frédéric Gibou
Chohong Min
Ron Fedkiw
Publikationsdatum
01.02.2013
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2-3/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-012-9660-1

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