A finite point method for adaptive three-dimensional compressible flow calculations

• Published in: International journal for numerical methods in fluids Vol. 60; no. 9; pp. 937 - 971
• Main Authors: Ortega, Enrique, Oñate, Eugenio, Idelsohn, Sergio
• Format: Journal Article Publication
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.07.2009; Wiley
• Subjects: 76 Fluid mechanics; Adaptivity; Anàlisi numèrica; Classificació AMS; Clouds; Collocation; Compressible flow; Computational methods in fluid dynamics; Elements finits; Elements finits, Mètode dels; Exact sciences and technology; Finite element method; Finite point method; Fluid dynamics; Flux de fluids; Fundamental areas of phenomenology (including applications); Física; Física de fluids; Matemàtiques i estadística; Mathematical analysis; Mathematical models; Mecànica de fluids; Meshfree methods (Numerical analysis); Meshless methods; Mètodes en elements finits; Numerical analysis; Physics; Three dimensional; Time integration explicit; Àrees temàtiques de la UPC; Compressible fluid; collocation; time integration explicit; Computational fluid dynamics; compressible flow; Digital simulation; Finite point method; Adaptive method; Upwind scheme; meshless methods; adaptivity; Three dimensional flow; Meshless method; Modelling; Collocation method; Time integration; Numerical convergence
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.1892

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.