Multigrid techniques as applied to gasdynamic simulation on unstructured meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1938-1952 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A multigrid method is proposed for solving the system of difference equations obtained via the finite-volume discretization of the Euler or Navier–Stokes equations on an unstructured mesh. A sequence of nested unstructured grids is generated via collapsing faces that take into account the features of the problem (inviscid/viscous). The capabilities of the approach are demonstrated by computing inviscid and viscous compressible uniform flows around an airfoil on structured, unstructured, and hybrid meshes. The topology of grids of different levels is described. Their quality and the influence of the grid structure on the convergence factor of the multigrid method are discussed.
@article{ZVMMF_2010_50_11_a7,
     author = {K. N. Volkov},
     title = {Multigrid techniques as applied to gasdynamic simulation on unstructured meshes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1938--1952},
     year = {2010},
     volume = {50},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a7/}
}
TY  - JOUR
AU  - K. N. Volkov
TI  - Multigrid techniques as applied to gasdynamic simulation on unstructured meshes
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1938
EP  - 1952
VL  - 50
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a7/
LA  - ru
ID  - ZVMMF_2010_50_11_a7
ER  - 
%0 Journal Article
%A K. N. Volkov
%T Multigrid techniques as applied to gasdynamic simulation on unstructured meshes
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1938-1952
%V 50
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a7/
%G ru
%F ZVMMF_2010_50_11_a7
K. N. Volkov. Multigrid techniques as applied to gasdynamic simulation on unstructured meshes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1938-1952. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a7/

[1] Fedorenko R. P., “Relaksatsionnyi metod resheniya raznostnykh ellipticheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 1:5 (1961), 922–927 | MR | Zbl

[2] Bakhvalov N. V., “O skhodimosti odnogo relaksatsionnogo metoda dlya ellipticheskogo operatora s estestvennymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 6:5 (1966), 101–135

[3] Astrakhantsev G. P., “Ob odnom relaksatsionnom metode”, Zh. vychisl. matem. i matem. fiz., 11:2 (1971), 439–448 | Zbl

[4] Brandt A., “Multi-level adaptive solutions to boundary value problems”, Math. of Comput., 31 (1977), 46–50 | DOI | MR

[5] Hackbusch W., Multigrid method and application, Springer-Verlag, Berlin, 1985, 377 pp. | MR | Zbl

[6] Jameson A., Schmidt W., Turkel E., Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes, AIAA Paper. No 81-1259, 1981 | Zbl

[7] Peraire J., Peiro J., Morgan K., “Finite element multigrid solution of Euler flows past installed aero-engines”, Comput. Mech., 11:5–6 (1993), 433–451 | DOI | Zbl

[8] Mavriplis D. J., “Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes”, J. Comput. Phys., 145:1 (1998), 141–165 | DOI | MR | Zbl

[9] Barth T. J., Aspects of unstructured grids and finite-volume solvers for the Euler and Navier–Stokes equations, VKI Lecture Series, 1994-05, Von Karman Institute for Fluid Dyanmics, Belgium, 1994, 124 pp.

[10] Moinier P., Muller J.-D., Giles M. B., “Edge-based multigrid and preconditioning for hybrid grids”, AIAA Journal, 40:10 (2002), 1954–1960 | DOI

[11] Crumpton P. I., Moinier P., Giles M. B., “An unstructured algorithm for high Reynolds number flows on highly stretched grids”, Numer. Meth. in Laminar and Turbulent Flows, Pineridge Press, 1997, 561–572

[12] Müller J.-D., Giles M. B., “Edge-based multigrid schemes for hybrid grids”, Numer. Meth. for Fluid Dynamics, 6 (1998), 425–432

[13] Moinier P., Giles M. B., “Preconditioned Euler and Navier–Stokes calculations on unstructured grids”, Proc. of the 6th ICFD Conf. on Num. Meth. for Fluid Dynamics (31 March–3 April 1998, Oxford, United Kingdom), 1998, 30

[14] Pierce N. A., Giles M. B., Jameson A., Martinelli L., Accelerating three-dimensional Navier–Stokes calculations, AIAA Paper. No 97-1953, 1997

[15] Volkov K. N., “Diskretizatsiya uravnenii Nave–Stoksa na nestrukturirovannoi setke pri pomoschi metoda kontrolnogo ob'ema i raznostnykh skhem povyshennoi razreshayuschei sposobnosti”, Zh. vychisl. matem. i matem. fiz., 48:7 (2008), 1250–1273

[16] Volkov K. N., “Primenenie metoda kontrolnogo ob'ema dlya resheniya zadach mekhaniki zhidkosti i gaza na nestrukturirovannykh setkakh”, Vychisl. metody i programmirovanie, 6:1 (2005), 43–60

[17] Cook P. H., McDonald M. A., Firmin G. N., Aerofil RAE2822 - pressure distribution and boundary layer and wake measurements, AGARD Advisory Reports. No AR-138, 1979