×

Approximate deconvolution models for magnetohydrodynamics. (English) Zbl 1410.76097

Summary: We consider the family of approximate deconvolution models (ADM) for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove the existence and uniqueness of solutions to the ADM-MHD equations, their weak converge to the solution of the MHD equations as the averaging radii tend to zero, and derive a bound on the modeling error. We demonstrate that the energy and helicity of the models are conserved, and the models preserve the Alfvén waves. We provide the results of the computational tests, that verify the accuracy and physical fidelity of the models.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76W05 Magnetohydrodynamics and electrohydrodynamics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adams N.A., Modern Simulation Strategies for Turbulent Flow (2001)
[2] DOI: 10.1038/150405d0 · doi:10.1038/150405d0
[3] Amrouche C., Czechoslovak Math. J. 44 pp 109– (1994)
[4] DOI: 10.1002/cpa.10072 · Zbl 1121.93306 · doi:10.1002/cpa.10072
[5] DOI: 10.1063/1.870270 · Zbl 1149.76316 · doi:10.1063/1.870270
[6] Berselli L.C., Scientific Computation (2006)
[7] Cowling T.G., Interscience Tracts on Physics and Astronomy (1957)
[8] Das A., DNS/LES Progress and Challenges pp 389– (2001)
[9] DOI: 10.1063/1.1516212 · Zbl 1185.76104 · doi:10.1063/1.1516212
[10] Davidson P.A., Cambridge Texts in Applied Mathematics (2001)
[11] DOI: 10.1137/S0036141003436302 · Zbl 1128.76029 · doi:10.1137/S0036141003436302
[12] Dunca A., DNS/LES Progress and Challenges pp 359– (2001)
[13] Dunca A., Contributions to Current Challenges in Mathematical Fluid Mechanics pp 53– (2004)
[14] Fursikov A.V., Theory and Applications. Translations of Mathematical Monographs 187 (2000)
[15] Gailitis A., Reports of the Physics Institute 12 pp 143– (1961)
[16] DOI: 10.1137/050624236 · Zbl 1354.49004 · doi:10.1137/050624236
[17] Grisvard P., Boundary Value Problems in Non-Smooth Domains (1980)
[18] DOI: 10.1090/S0025-5718-1991-1066834-0 · doi:10.1090/S0025-5718-1991-1066834-0
[19] Gunzburger M.D., Int. J. Pure Appl. Math. 42 pp 289– (2008)
[20] DOI: 10.1016/j.jmaa.2004.11.022 · Zbl 1073.49003 · doi:10.1016/j.jmaa.2004.11.022
[21] DOI: 10.1063/1.868525 · doi:10.1063/1.868525
[22] DOI: 10.1063/1.868525 · doi:10.1063/1.868525
[23] John V., Lecture Notes in Computational Science and Engineering 34 (2004)
[24] Labovschii A., Quality and Reliability of Large-Eddy Simulations (2007)
[25] Labovschii A., J. Math. Anal. Appl.
[26] Landau L., Électrodynamique des Milieux Continus (1969)
[27] Layton W., Numer. Funct. Anal. Optim. (2010)
[28] Layton W., Mathematical and Computer Modelling
[29] DOI: 10.1007/BF02547354 · JFM 60.0726.05 · doi:10.1007/BF02547354
[30] Lions J.L., Quelques méthodes de Résolution des Problèmes aux Limites Non Linéaires (1969)
[31] Meng J.C.S., Sea Technology 33 pp 29– (1992)
[32] Meng J.C.S., Magnetohydrodynamics 30 pp 401– (1994)
[33] DOI: 10.1007/BF02657377 · doi:10.1007/BF02657377
[34] DOI: 10.1016/j.ocemod.2008.09.006 · doi:10.1016/j.ocemod.2008.09.006
[35] DOI: 10.1115/1.2910680 · doi:10.1115/1.2910680
[36] Sagaut P., Large Eddy Simulation for Incompressible Flows, ed., 3. ed. (2006) · Zbl 1091.76001
[37] DOI: 10.1007/BF02657737 · doi:10.1007/BF02657737
[38] DOI: 10.1002/cpa.3160360506 · Zbl 0524.76099 · doi:10.1002/cpa.3160360506
[39] Shercliff J.A., A Textbook of Magnetohydrodynamics (1965)
[40] DOI: 10.1115/1.2819508 · doi:10.1115/1.2819508
[41] Tartar L., Publications Mathématiques d’Orsay (1978)
[42] R. Temam ( 1995 ). Navier–Stokes Equations and Nonlinear Functional Analysis . CBMS-NSF Regional Conference Series in Applied Mathematics , Society for Industrial and Applied Mathematics , Philadelphia . · Zbl 0833.35110
[43] Tsinober A., Viscous Drag Reduction in Boundary Layers (1990)
[44] Tsinober A.B., Magnetohydrodynamics 3 pp 152– (1967)
[45] DOI: 10.1007/BF02679714 · doi:10.1007/BF02679714
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.