Explicit and implicit meshless methods for linear advection-diffusion type of partial differential equations
Explicit and implicit meshless methods for linear advection-diffusion type of partial differential equations
Simple, mesh/grid free, explicit and implicit numerical schemes for the solution of linear advection-diffusion problems is developed and validated herein. Unlike the mesh or grid-based methods, these schemes use well distributed quasi-random points and approximate the solution using global radial basis functions. The schemes can be seen as generalized finite differences with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties.
meshless methods, collocation, radial basis functions, random points, advection-diffusion, partial differential equations
19-35
Zerroukat, M.
7fc5b20d-0034-42b7-be98-6fbfae8158c2
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Charafi, A.
5e8eefa9-8c99-4c39-a667-0c071733fa5b
2000
Zerroukat, M.
7fc5b20d-0034-42b7-be98-6fbfae8158c2
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Charafi, A.
5e8eefa9-8c99-4c39-a667-0c071733fa5b
Abstract
Simple, mesh/grid free, explicit and implicit numerical schemes for the solution of linear advection-diffusion problems is developed and validated herein. Unlike the mesh or grid-based methods, these schemes use well distributed quasi-random points and approximate the solution using global radial basis functions. The schemes can be seen as generalized finite differences with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties.
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zerr_00.pdf
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Published date: 2000
Keywords:
meshless methods, collocation, radial basis functions, random points, advection-diffusion, partial differential equations
Identifiers
Local EPrints ID: 21531
URI: http://eprints.soton.ac.uk/id/eprint/21531
ISSN: 0029-5981
PURE UUID: bd67da50-c0fa-448b-a9b7-5945994dc0c3
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Date deposited: 08 Feb 2007
Last modified: 15 Mar 2024 06:31
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Author:
M. Zerroukat
Author:
A. Charafi
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