A Conservative Mesh-Free Scheme and Generalized Framework for Conservation Laws
Name
Chiu-2012-A CONSERVATIVE MESH-FREE SCHEME.pdf
Size
792.88 KB
Format
Adobe PDF
Checksum (MD5)
26a5abe8c1a8ca160897e1944a248bd2
Author(s)
Chiu, Edmond Kwan-Yu
Wang, Qiqi
Hu, Rui
Jameson, Antony
Date Issued
November 2012
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Kwan-yu Chiu, Edmond et al. “A Conservative Mesh-Free Scheme and Generalized Framework for Conservation Laws.” SIAM Journal on Scientific Computing 34.6 (2012): A2896–A2916. © 2012, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We present a novel mesh-free scheme for solving partial differential equations. We first derive a conservative and stable formulation of mesh-free first derivatives. We then show that this formulation is a special case of a general conservative mesh-free framework that allows flexible choices of flux schemes. Necessary conditions and algorithms for calculating the coefficients for our mesh-free schemes that satisfy these conditions are also discussed. We include numerical examples of solving the one- and two-dimensional inviscid advection equations, demonstrating the stability and convergence of our scheme and the potential of using the general mesh-free framework to extend finite volume discretization to a mesh-free context.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/110842740
