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Computational Mechanics
Erschienen in: Computational Mechanics 2/2017

03.04.2017 | Original Paper

A-posteriori error estimation for the finite point method with applications to compressible flow

verfasst von: Enrique Ortega, Roberto Flores, Eugenio Oñate, Sergio Idelsohn

Erschienen in: Computational Mechanics | Ausgabe 2/2017

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Abstract

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.
Vorheriger Artikel On the stress calculation within phase-field approaches: a model for finite deformations
Nächster Artikel An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints

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Literatur
1.
Roache PJ (1997) Quantification of uncertainty in computational fluid dynamics. Annu Rev Fluid Mech 29:123–160MathSciNetCrossRef
2.
Oberkampf WL, Trucano TG (2002) Verification and validation in computational fluid dynamics. Prog Aerosp Sci 38:209–272CrossRef
3.
Roy CJ (2005) Review of code and solution verification procedures for computational simulation. J Comput Phys 205:131–156CrossRefMATH
4.
Thacker BH et al (2004) Concepts of model verification and validation. Los Alamos National Laboratory, LA-14167-MS
5.
Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24:337–357MathSciNetCrossRefMATH
6.
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and a-posteriori error estimates. Part 2: error estimates and adaptivity. Int J Numer Methods Eng 33:1365–1382CrossRefMATH
7.
Babuska I, Miller A (1984) Post-processing approach in the finite element method. Part 3: a-posteriori error estimates and adaptive mesh selection. Int J Numer Methods Eng 20(12):2311–2324CrossRefMATH
8.
Oden JT, Wu W, Ainsworth M (1993) An a-posteriori error estimate for finite element approximations of the Navier–Stokes equations. Comput Methods Appl Mech Eng 111:185–202MathSciNetCrossRefMATH
9.
Chang S, Haworth DC (1997) Adaptive grid refinement using cell-level and global imbalances. Int J Numer Methods Fluids 24:375–392CrossRefMATH
10.
Oden JT, Prudhomme S (1999) New approaches to error estimation and adaptivity for the Stokes and Oseen equations. Int J Numer Methods Fluids 31:3–15MathSciNetCrossRefMATH
11.
Oñate E et al (2006) Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach. Comput Methods Appl Mech Eng 195:339–362MathSciNetCrossRefMATH
12.
Venditti DA, Darmofal DL (2000) Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one dimensional flow. J Comput Phys 164:204–227MathSciNetCrossRefMATH
13.
Fidkowski KJ, Darmofal DL (2011) Review of output-based error estimation and mesh adaptation in computational fluid dynamics. AIAA J 49(4):673–694CrossRef
14.
Dwight RP (2008) Heuristic a-posteriori estimation of error due to dissipation in finite volume schemes with application to mesh adaptation. J Comput Phys 227(5):2845–2863CrossRefMATH
15.
Zhang XD, Trépanier JY, Camarero R (2000) A posteriori error estimation for finite-volume solutions of hyperbolic conservation laws. Comput Methods Appl Mech Eng 185:1–19MathSciNetCrossRefMATH
16.
Hay A, Visonneau M (2006) Error estimation using the error transport equation for finite-volume methods and arbitrary meshes. Int J Comput Fluid Dyn 20(7):463–479MathSciNetCrossRefMATH
17.
Shih T, Qin Y (2007) A-posteriori method for estimating and correcting grid-induced errors in CFD solutions. Part 1: theory and method. AIAA Paper 2007-100
18.
Roy CJ (2009) Strategies for driving mesh adaption in CFD. AIAA Paper 2009-1302
19.
Muzaferija S, Gosman D (1996) Finite-volume CFD procedure and adaptive error control strategy for grids of arbitrary topology. J Comput Phys 138:766–787MathSciNetCrossRefMATH
20.
Blottner FG, Lopez AR (1998) Determination of solution accuracy of numerical schemes as part of code and calculation verification. SANDIA report SAND98-2222
21.
22.
23.
Aftosmis MJ, Berger M (2002) Multilevel error estimation and adaptive h-refinement for cartesian meshes with embedded boundaries. AIAA Paper 2002-0863
24.
Fulton SR (2003) On the accuracy of multigrid truncation error estimates. Electron Trans Numer Anal 15:29–37MathSciNetMATH
25.
Gao H, Wang ZJ (2011) A residual-based procedure for hp-adaptation on 2D hybrid meshes. AIAA Paper 2011-492
26.
Richardson LF (1910) The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Philos Trans R Soc Lond Ser A 210(459–470):307–357MATH
27.
Richardson LF, Gaunt JA (1927) The deferred approach to the limit. Philos Trans R Soc Lond Ser A 226(636–646):299–349CrossRefMATH
28.
Cadafalch J et al (2002) Verification of finite volume computations on steady-state fluid flow and heat transfer. J Fluids Eng 124:11–21CrossRef
29.
Roy CJ, Blottner FG (2003) Methodology for turbulence model validation: application to hypersonic flows. J Spacecr Rockets 40(3):313–325CrossRef
30.
Roy CJ (2003) Grid convergence error analysis for mixed-order numerical schemes. AIAA J 41:595–604CrossRef
31.
Salas MD (2006) Some observations on grid convergence. Comput Fluids 35:688–692
32.
Roache PJ (1994) Perspective: a method for uniform reporting of grid refinement studies. J Fluids Eng 116:405–413CrossRef
33.
Barth TJ (1991) A 3D upwind euler solver for unstructured meshes. AiAA Paper 1991-1548
34.
Zhang Z, Naga A (2005) A new finite element gradient recovery method: superconvergence property. SIAM J Sci Comput 26(4):1192–1213MathSciNetCrossRefMATH
35.
Cueto-Felgueroso L et al (2007) Finite volume solvers and moving least-squares approximations for the compressible Navier–Stokes equations on unstructured grids. Comput Methods Appl Mech Eng 196(45–48):4712–4736MathSciNetCrossRefMATH
36.
37.
Liu WK et al (1997) Multiresolution reproducing kernel particle method for computational fluid dynamics. Int J Numer Methods Fluids 24(12):1391–1415MathSciNetCrossRefMATH
38.
Gavete L, Cuesta JL, Ruiz A (2002) A numerical comparison of two different approximations of the error in a meshless method. Eur J Mech Solids 21:1037–1054CrossRefMATH
39.
Lee CK, Zhou CE (2004) On error estimation and adaptive refinement for element free Galerkingmethod. Part I: stress recovery and a posteriori error estimation. Comput Struct 82:413–428CrossRef
40.
Rabczuk T, Belytschko T (2005) Adaptivity for structured meshfree particle methods in 2D and 3D. Int J Numer Methods Eng 63:1559–1582MathSciNetCrossRefMATH
41.
Li Q, Lee K-M (2006) An adaptive meshless method for magnetic field computation. IEEE Trans Magn 42(8):1996–2003CrossRef
42.
Angulo A, Pérez Pozo L, Perazzo F (2009) A posteriori error estimator and an adaptive technique in meshless finite point method. Eng Anal Bound Elem 33(11):1322–1338MathSciNetCrossRefMATH
43.
You Y, Chen JS, Lu H (2003) Filters, reproducing kernel, and adaptive meshfree method. Comput Mech 31(3–4):316–326MATH
44.
Perazzo F, Löhner R, Perez-Pozo L (2007) Adaptive methodology for meshless finite point method. Adv Eng Softw 39:156–166CrossRef
45.
Afshar MH, Lashckarbolok M (2008) Collocated discrete least-squares (CDLS) meshless method: error estimate and adaptive refinement. Int J Numer Methods Fluids 56:1909–1928CrossRefMATH
46.
47.
Rüter M, Chen JS (2015) A multi-space error estimation approach for meshfree methods. In: Conference applications of mathematics 2015. Prague
48.
Oñate E et al (1996) A stabilized Finite Point Method for analysis of fluid mechanics problems. Comput Methods Appl Mech Eng 139:315–346MathSciNetCrossRefMATH
49.
Löhner R et al (2002) A Finite Point Method for compressible flow. Int J Numer Methods Eng 53:1765–1779CrossRefMATH
50.
Ortega E, Oñate E, Idelsohn S (2009) A finite point method for adaptive three-dimensional compressible flow calculations. Int J Numer Methods Fluids 60:937–971MathSciNetCrossRefMATH
51.
Ortega E, Oñate E, Idelsohn S (2007) An improved finite point method for three-dimensional potential flows. Comput Mech 40:949–963MathSciNetCrossRefMATH
52.
Ortega E et al (2014) Comparative accuracy and performance assessment of the finite point method in compressible flow problems. Comput Fluids 59:53–65MathSciNetCrossRef
53.
Fischer T (1996) A contribution to adaptive numerical solution of compressible flow problems. Universitat Politècnica de Catalunya, BarcelonaMATH
54.
55.
Katz A (2009) Meshless methods for computational fluid dynamics. ProQuest dissertations and theses, Thesis (Ph.D.), Stanford University
56.
Ortega E, Oñate E, Idelsohn S, Flores R (2014) Comparative accuracy and performance assessment of the Finite Point Method in compressible flow problems. Comput Fluids 89:53–65MathSciNetCrossRef
57.
58.
Turkel E (1988) Improving the accuracy of central difference schemes. ICASE Report 88-53
59.
Van Albada GD, Van Leer B, Roberts WWJ (1982) A comparative study of computational methods in cosmic gas dynamics. Astron Astrophys 108:76–84MATH
60.
Jameson A (1993) Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows. AIAA-93-3359
61.
Jameson A, Baker TJ (1987) Improvements to the aircraft Euler method. AIAA Paper 87-0452
62.
Van Leer B (1979) Towards the ultimate conservative difference scheme. V, A second order sequel to Godunov’s method. J Comput Phys 32:101–136CrossRefMATH
63.
Berger M, Aftosmis MJ (2005) Analysis of slope limiters on irregular grids. AIAA Paper 2005-0490
64.
65.
66.
Qiu J, Shu C (2003) Hermite WENO schemes and their application as limiters for the Runge–Kutta discontinuous Galerking method: one dimensional case. J Comput Phys 193:115–135CrossRefMATH
67.
68.
Zienkiewicz OC, Taylor RL (2000) The finite element method, vol 1. Butterworth-Heinemann, OxfordMATH
69.
Ortega E et al (2013) A meshless finite point method for three-dimensional analysis of compressible flow problems involving moving boundaries and adaptivity. Int J Numer Methods Fluids 73(4):323–343MathSciNetCrossRef
70.
Loving D, Estabrooks B (1951) Transonic-wing investigation in the Langley 8-foot high-speed tunnel at high subsonic Mach numbers and at a Mach number of 1.2. Analysis of pressure distribution of wing-fuselage configuration having a wing of \(45^{{\rm o}}\) sweepback, aspect ratio 4, taper ratio 0.6, and NACA 65A006 airfoil section. National Advisory Committee for Aeronautics. Research Memorandum NACA RM L51F07
Metadaten
Titel
A-posteriori error estimation for the finite point method with applications to compressible flow
verfasst von
Enrique Ortega
Roberto Flores
Eugenio Oñate
Sergio Idelsohn
Publikationsdatum
03.04.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 2/2017
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-017-1402-7

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