A finite point method for compressible flow

A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the...

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Published inInternational journal for numerical methods in engineering Vol. 53; no. 8; pp. 1765 - 1779
Main Authors Löhner, Rainald, Sacco, Carlos, Oñate, Eugenio, Idelsohn, Sergio
Format Journal Article Publication
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 20.03.2002
John Wiley & sons
Subjects
Online AccessGet full text
ISSN0029-5981
1097-0207
1097-0207
DOI10.1002/nme.334

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Abstract A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive. Copyright © 2001 John Wiley & Sons, Ltd.
AbstractList This is the accepted version of the following article: [Löhner, R. , Sacco, C. , Oñate, E. and Idelsohn, S. (2002), A finite point method for compressible flow. Int. J. Numer. Meth. Engng., 53: 1765-1779. doi:10.1002/nme.334], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.334 A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based finite volume or finite element techniques, making the present finite point method competitive. Peer Reviewed
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive. Copyright © 2001 John Wiley & Sons, Ltd.
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based finite volume or finite element techniques, making the present finite point method competitive. (Author)
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based finite volume or finite element techniques, making the present finite point method competitive.
Author Sacco, Carlos
Löhner, Rainald
Idelsohn, Sergio
Oñate, Eugenio
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References_xml – reference: Samet H. The quadtree and related hierarchical data structures. Computing Surveys 1984; 16(2):187-285.
– reference: Godunov SK. Mat. Sb. 1959; 47:271-306.
– reference: Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, Uras RA, Chang CT. Overview and applications of the reproducing Kernel particle methods. Archives of Computational Methods in Engineering 1996; 3(1):3-80.
– reference: Knuth DN. The Art of Computer Programming vols. 1-3. Addison-Wesley: Reading, MA, 1973.
– reference: George PL, Borouchaki H (eds). Delaunay Triangulation and Meshing. Hermes: Paris, 1998.
– reference: Sweby PK. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal of Numerical Analysis 1984; 21:995-1011.
– reference: Belytschko T, Lu Y, Gu L. Element free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
– reference: Luo H, Baum JD, Löhner R. Edge-based finite element scheme for the Euler equations. AIAA J 1994; 32(6):1183-1190.
– reference: Oñate E, Idelsohn S. A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Computational Mechanics 1998; 21:283-292.
– reference: Oñate E, Sacco C, Idelsohn S. A finite point method for incompressible flow problems. Comput. and Visual Science 2000; 3:67-75.
– reference: van Leer B. Towards the ultimate conservative scheme II. Monotonicity and conservation combined in a second order scheme. Journal of Computational Physics 1974; 14:361-370.
– reference: Atluri SN, Kim HG, Cho JY. A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Computational Mechanics 1999; 24:348-372.
– reference: Löhner R. Some useful data structures for the generation of unstructured grids. Communications in Applied Numerical Methods 1988; 4:123-135.
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– reference: Hirsch C. Numerical Computation of Internal and External Flow. Wiley: New York, 1991.
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  year: 2000
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  article-title: A finite point method for incompressible flow problems
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– volume: 139
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Snippet A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a...
This is the accepted version of the following article: [Löhner, R. , Sacco, C. , Oñate, E. and Idelsohn, S. (2002), A finite point method for compressible...
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SubjectTerms Anàlisi numèrica
CFD
Compressible Flows
Computational fluid dynamics
Dinàmica de fluids computacional
Finite Point Methods
Física
Física de fluids
Matemàtiques i estadística
Mesh Free Techniques
Mètodes en elements finits
Àrees temàtiques de la UPC
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Title A finite point method for compressible flow
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