View : 91 Download: 0

Convergence analysis on the Gibou-Min method for the Hodge projection

Title
Convergence analysis on the Gibou-Min method for the Hodge projection
Authors
Yoon G.Park J.-H.Min C.
Ewha Authors
민조홍
SCOPUS Author ID
민조홍scopus
Issue Date
2017
Journal Title
Communications in Mathematical Sciences
ISSN
1539-6746JCR Link
Citation
Communications in Mathematical Sciences vol. 15, no. 5, pp. 1211 - 1220
Keywords
Finite volume methodGibou-MinHodge projectionPoisson equation
Publisher
International Press of Boston, Inc.
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
The Hodge projection of a vector field is the divergence-free component of its Helmholtz decomposition. In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. In the decomposition by the Gibou-Min method, an important L2-orthogonality holds between the gradient field and the solenoidal field, which is similar to the continuous Hodge decomposition. Using the orthogonality, we present a novel analysis which shows that the convergence order is 1.5 in the L2-norm for approximating the divergence-free vector field. Numerical results are presented to validate our analyses. © 2017 International Press.
DOI
10.4310/CMS.2017.v15.n5.a2
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE