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A finite point method for adaptive three‐dimensional compressible flow calculations
Author(s) -
Ortega Enrique,
Oñate Eugenio,
Idelsohn Sergio
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1892
Subject(s) - solver , regularized meshless method , compressible flow , moving least squares , mathematics , flow (mathematics) , compressibility , computational fluid dynamics , mathematical optimization , numerical analysis , collocation method , computer science , point (geometry) , point cloud , computation , algorithm , finite element method , mathematical analysis , geometry , singular boundary method , mechanics , artificial intelligence , differential equation , physics , ordinary differential equation , boundary element method , thermodynamics
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h ‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.