Geodesic
The impact of grid geometry on the accuracy of higher order finite-volume and finite-element schemes
Matematičeskoe modelirovanie, Tome 22 (2010) no. 3, pp. 145-160.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the issues of a higher-order finite-volume and finite-element discretization on anisotropic grids. It will be shown that high order finite-volume schemes are inferior to finite-element schemes in terms of accuracy when stretched meshes are considered. The poor accuracy of finite-volume schemes is discussed based on the idea of numerically distant points that are present in a reconstruction stencil on stretched meshes. 
@article{MM_2010_22_3_a9,
     author = {N. B. Petrovskaya and A. V. Wolkov},
     title = {The impact of grid geometry on the accuracy of higher order finite-volume and finite-element schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {145--160},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_3_a9/}
}
TY  - JOUR
AU  - N. B. Petrovskaya
AU  - A. V. Wolkov
TI  - The impact of grid geometry on the accuracy of higher order finite-volume and finite-element schemes
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 145
EP  - 160
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_3_a9/
LA  - ru
ID  - MM_2010_22_3_a9
ER  - 
%0 Journal Article
%A N. B. Petrovskaya
%A A. V. Wolkov
%T The impact of grid geometry on the accuracy of higher order finite-volume and finite-element schemes
%J Matematičeskoe modelirovanie
%D 2010
%P 145-160
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_3_a9/
%G ru
%F MM_2010_22_3_a9
N. B. Petrovskaya; A. V. Wolkov. The impact of grid geometry on the accuracy of higher order finite-volume and finite-element schemes. Matematičeskoe modelirovanie, Tome 22 (2010) no. 3, pp. 145-160. http://geodesic.mathdoc.fr/item/MM_2010_22_3_a9/

[1] A. V. Volkov, S. V. Lyapunov, “Issledovanie effektivnosti ispolzovaniya chislennykh skhem vysokogo poryadka tochnosti dlya resheniya uravnenii Nave–Stoksa i Reinoldsa na nestrukturirovannykh adaptivnykh setkakh”, ZhVMiMF, 46:10 (2006), 1894–1907 | MR

[2] M. B. Bieterman, J. E. Bussoletti, C. L. Hilmes, F. T. Johnson, R. G. Melvin, D. P. Young, “An Adaptive Grid Method for Analysis of 3D Aircraft Configurations”, Computer Methods in Applied Mechanics and Engineering, 101 (1992), 225–249 | DOI | Zbl

[3] D. L. Darmofal, R. Haimes, Towards the Next Generation in CFD, AIAA 2005–0087

[4] T. Barth, P. Frederickson, Higher-Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction, AIAA 90–0013, 1990

[5] T. J. Barth, “Numerical Methods for Gasdynamic Systems on Unstructured Meshes”, Lecture Notes in Comput. Sci. Engrg., 8, 1998, 195–284 | MR

[6] V. Venkatakrishnan, S. Allmaras, D. Kamenetskii, F. Johnson, Higher Order Schemes for the Compressible Navier–Stokes Equations, AIAA 2003–3987, 2003 | Zbl

[7] Ch. Hirsch, Numerical Computation of Internal and External Flows, John Wiley Son, Ltd, 1990, 714 pp. | Zbl

[8] T. J. Barth, D. C. Jespersen, The Design and Application of Upwind Schemes on Unstructured Meshes, AIAA 89–0366, 1989

[9] C. Ollivier-Gooch, M. Van Altena, “A High-Order-Accurate Unstructured Mesh Finite-Volume Scheme for the Advection-Diffusion Equation”, J. Comp. Phys., 181 (2002), 729–752 | DOI | Zbl

[10] A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 608 pp. | MR

[11] F. Bassi, S. Rebay, “A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressile Navier–Stokes Equations”, J. Comput. Phys., 131:2 (1997), 267–279 | DOI | MR | Zbl

[12] B. Cockburn, G. E. Karniadakis, C.-W. Shu, “The Development of Discontinuous Galerkin Methods”, Lecture Notes in Comput. Sci. Engrg., 11, 2000, 3–50 | MR | Zbl

[13] T. J. R. Hughes, A. Brooks, “A Multidimensional Upwind Scheme with no Crosswind Diffusion”, Finite Element Methods for Convection Dominated Flows, ASME, New York, 1979 | MR | Zbl

[14] R. K. Agarwal, D. W. Halt, “A Compact High-Order Unstructured Grids Method for the Solution of Euler Equations”, Int. J. Num. Meth. Fluids, 31 (1999), 121–147 | 3.0.CO;2-S class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[15] D. Vigneron, J.-M. Vaassen, J. A. Essers, “An Implicit High Order Cell-Centered Finite Volume Scheme for the Solution of Three-Dimensional Navier–Stokes Equations on Unstructured Grids”, Third MIT Conference on Computational Fluid and Solid Mechanics, MA, USA, 2003

[16] G. F. Carey, Computational Grids: Generation, Adaptation, and Solution Strategies, Taylor Francis, 1997, 496 pp. | MR | Zbl

[17] W. K. Anderson, “A Grid Generation and Flow Solution Method for the Euler Equations on Unstructured Grids”, J. Comput. Phys., 110:1 (1994), 23–38 | DOI | Zbl

[18] S. J. Sherwin, J. Peiro, “Mesh Generation in Curvilinear Domains Using High-Order Elements”, Int. J. Num. Meth. Engrg., 53 (2002), 207–223 | DOI | Zbl

[19] A. N. Gilmanov, Metody adaptivnykh setok v zadachakh gazovoi dinamiki, Nauka, M., 2000, 240 pp. | MR

[20] A. S. Lebedev, V. D. Liseikin, G. S. Khakimzyanov, “Razrabotka metodov postroeniya adaptivnykh setok”, Vychislitelnye tekhnologii, 7:3 (2002), 29–43 | MR | Zbl

[21] A. A. Martynov, S. Yu. Medvedev, “Nadezhnyi cposob postroeniya setok s vytyanutymi yacheikami”, Postroenie raschetnykh setok: teoriya i prilozheniya, sb., eds. S. A. Ivanenko, V. A. Garanzha, VTs RAN, Moskva, 2002, 266–276

[22] N. B. Petrovskaya, “Modification of a Finite Volume Scheme for Laplace's Equation”, SIAM J. Sci. Comput., 23:3 (2001), 891–909 | DOI | MR | Zbl

[23] W. H. Reed, T. R. Hill, Triangular Mesh Methods for the Neutron Transport Equation, Technical Report LA–UR–73–479, Los Alamos National Laboratory, Los Alamos, New Mexico, 1973

[24] N. B. Petrovskaya, “Vybor vesovykh koeffitsientov v zadache approksimatsii gradienta metodom naimenshikh kvadratov”, Matematich. modelirovanie, 16:5 (2004), 83–93 | MR

[25] N. N. Kalitkin, Chislennye metody, Nauka, M., 1978, 272 pp. | MR

[26] D. J. Mavriplis, Revisiting the Least-Square Procedure for Gradient Reconstruction on Unstructured Meshes, AIAA 2003–3986, 2003 | Zbl

[27] N. B. Petrovskaya, “Discontinuous Weighted Least-Squares Approximation on Irregular Grids”, CMES: Computer Modeling in Engineering and Sciences, 32:2 (2008), 69–84 | MR