A finite element modified method of characteristics for convective heat transport. (English) Zbl 1143.65075
Summary: We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier-Stokes equations including density variation through the Boussinesq approximation. The solution procedure consists of combining an essentially non-oscillatory modified method of characteristics for time discretization with finite element method for space discretization. These numerical techniques associate the geometrical flexibility of the finite elements with the ability offered by modified method of characteristics to solve convection-dominated flows using time steps larger than its Eulerian counterparts. Numerical results are shown for natural convection in a squared cavity and heat transport in the strait of Gibraltar. Performance and accuracy of the method are compared to other published data.
MSC:
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
Keywords:
convection-dominated flows; essentially nonoscillatory interpolation; finite element method; incompressible Navier-Stokes equations; modified method of characteristics; natural convection; comparison of methodsReferences:
| [1] | Douglas, SIAM J Numer Anal 19 pp 871– (1982) |
| [2] | Pironneau, Numer Math 38 pp 309– (1982) |
| [3] | Süli, Numer Math 53 pp 1025– |
| [4] | Bause, SIAM J Numer Anal 39 pp 1954– (2002) |
| [5] | Morton, Math Model Numer Anal 22 pp 625– (1988) |
| [6] | Priestley, J Comp Phys 112 pp 316– (1994) |
| [7] | El-Amrani, Commun Numer Meth Eng 22 pp 831– (2006) |
| [8] | Seaïd, Comp Methods App Math 2 pp 392– (2002) |
| [9] | Seaïd, Comp Methods Appl Math 2 pp 186– (2002) |
| [10] | Bermejo, J Comp Appl Math 154 pp 27– (2003) |
| [11] | El-Amrani, J Numer Math |
| [12] | Boris, J Comp Phys 35 pp 172– (1997) |
| [13] | Zalesak, J Comp Phys 31 pp 335– (1979) |
| [14] | Seaïd, Comput Visual Sci 9 pp 209– (2006) |
| [15] | Temperton, Quart J Roy Meteor Soc 113 pp 1025– (1988) |
| [16] | Giraldo, J Comp Phys 147 pp 114– (1998) |
| [17] | Kaazempur-Mofrad, Comp Methods Appl Mech Eng 191 pp 5345– (2002) |
| [18] | Allievi, J Comp Phys 132 pp 157– (1997) |
| [19] | Bercovier, Numer Math 33 pp 211– (1979) |
| [20] | Verfürth, RAIRO Anal Numer 18 pp 175– (1984) |
| [21] | and , On some finite elements methods for the numerical simulation of incompressible viscous flow, Incompressible computational fluid dynamics, Cambridge University Press, and , editors, Cambridge, 1993. |
| [22] | Numerical solution of partial differential equations by the finite element method, Cambridge University Press, Cambridge-Lund, 1987. |
| [23] | De Valhl Davis, Int J Numer Meth Fluids 3 pp 249– (1983) |
| [24] | Manzari, Int J Numer Method Heat Fluid Flow 9 pp 860– (1999) |
| [25] | Mayne, Int J Numer Meth Heat Fluid Flow 10 pp 598– (2000) |
| [26] | Wan, Numer Heat Transfer Part B 40 pp 199– (2001) |
| [27] | , , and , editors, Seminario Sobre la Oceanografía Física del Estrecho de Gibraltar, SECEG, Madrid, 1988. |
| [28] | Millán, Atmos Res 36 pp 1– (1995) |
| [29] | Polyak, Tectonophysics 263 pp 191– (1996) |
| [30] | González, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 11 pp 383– (1995) |
| [31] | Seaïd, Lect Notes Comput Sci 3037 pp 89– (2004) |
| [32] | González, Prog Ind Math 8 pp 518– (2005) |
| [33] | MacDonald, Monthly Weather Rev 128 pp 4084– (2000) |
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.
