An operator splitting numerical scheme for thermal/isothermal incompressible viscous flows

Bermúdez, Blanca; Nicolás, Alfredo

doi:10.1002/(sici)1097-0363(19990228)29:4<397::aid-fld793>3.0.co;2-n

Cited by 12 publications

(12 citation statements)

References 14 publications

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“…Figures 3 and 4 show the ows for Reynolds number Re = 1000 and Grashof numbers Gr = 10 2 and Gr = 10 6 in the unit square cavity on a mesh (h x ; h y ) = (1=120; 1=120), both with t = 0:01; the streamlines on the left are obtained with the contour values given by Ghia et al [15] whereas the isotherms on the right are 'default' ones. Both results agree with those in Reference [6]; they in turn were validated with the ones in Reference [14]. The validation from this work is reinforced by showing in Figure 5 the proÿles of the horizontal U and vertical V component of the velocity at x = 0:5 (left) and y = 0:5 (right), respectively, for Gr = 10 6 ÿxed and Re = 400, 1000, 3000, with their min-max values given in Table I.…”

Section: Mixed Convection Thermal Owssupporting

confidence: 93%

“…Taking into account that the elliptic system (10), in addition to being non-linear, is of the non-potential (or transport) type, a ÿxed point iterative process is used for the solution. This process is similar to one applied previously to mixed convection problems in primitive variables [6]. A distinctive aspect here is that the iterative process is extended up to the boundary to handle the !…”

Section: Numerical Schemementioning

confidence: 99%

“…(1) Gr = 10 2 1 107.65 (2) Gr = 10 6 1 372.97 (3) Gr = 10 6 2 1097.09 (4) Gr = 10 6 3 1511.41 (5) Gr = 10 7 1 430.26…”

Section: A Ratio Tssmentioning

confidence: 99%

“…(x; 0) = ! 0 (x) and Â(x; 0) = Â 0 (x) denote the initial conditions for the vorticity and for the temperature, respectively; the initial vorticity, by (6) has to satisfy ! 0 = @u 02 =@x − @u 01 =@y if u 0 = (u 01 ; u 02 ) is the initial velocity.…”

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confidence: 99%

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2D thermal/isothermal incompressible viscous flows

Nicolás¹,

Bermúdez²

2005

Int. J. Numer. Meth. Fluids

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1 Depto. MatemÃ aticas; 3er. Piso Ed. AT-Diego Bricio; UAM-Iztapalapa; 09340 MÃ exico D.F.; MÃ exico 2 Facultad de C. de la ComputaciÃ on; BUAP; Pue.; MÃ exico SUMMARY 2D thermal and isothermal time-dependent incompressible viscous ows are presented in rectangular domains governed by the Boussinesq approximation and Navier-Stokes equations in the stream function-vorticity formulation. The results are obtained with a simple numerical scheme based on a ÿxed point iterative process applied to the non-linear elliptic systems that result after a second-order time discretization. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the ÿrst time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state ows obtained from the unsteady problem.

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Section: Mixed Convection Thermal Owssupporting

confidence: 93%

Section: Numerical Schemementioning

confidence: 99%

“…(1) Gr = 10 2 1 107.65 (2) Gr = 10 6 1 372.97 (3) Gr = 10 6 2 1097.09 (4) Gr = 10 6 3 1511.41 (5) Gr = 10 7 1 430.26…”

Section: A Ratio Tssmentioning

confidence: 99%

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confidence: 99%

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2D thermal/isothermal incompressible viscous flows

Nicolás¹,

Bermúdez²

2005

Int. J. Numer. Meth. Fluids

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“…The analysis concentrated mostly on the validation and physical correctness of the obtained solutions, although the numerical efficiency was also addressed. In the other publication (Bermudez and Nicolas, 1999), a fractional-time-step algorithm has been proposed for unsteady thermally-coupled flows. In this approach, the main time step is divided into three equal sub-steps.…”

Section: Introductionmentioning

confidence: 99%

Unconditionally stable numerical scheme for natural convection problems

Górecki

Szumbarski

2014

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -Both the importance of the natural convection in science and engineering and the shortage of publications in the field of numerical features of time-stepping schemes for the simulation of coupled heat and fluid flow problems motivate the present work. The paper aims to discuss these issues. Design/methodology/approach -The paper presents the unconditionally stable time-stepping scheme for simulation of coupled problems of mass and heat transport. The paper is divided into two parts. The first part concerns the mathematical formulation of the scheme and discusses its implementation. The second part focuses on the numerical simulation and its results. A detailed investigation of the temporal order of the scheme with respect to the L2-norms of the errors of the pressure, velocity, temperature and divergence of velocity fields has also been given. Findings -The work shows that it is possible to formulate a numerical scheme which is unconditionally stable with respect to the time step size. Moreover, application of the spectral element method for the spatial discretization results in a high order of approximation in space and very good overall accuracy. Furthermore, the investigation of the numerical features of the scheme showed that the formal temporal order of the scheme (formally second order) has been deferred very slightly and the order of 1.8-1.9 is achieved for all unknown fields. Originality/value -The paper presents a new unconditionally stable scheme for simulation of unsteady flows with bidirectional coupling of heat transfer and the fluid flow. It also carefully investigates the numerical behaviour of the method.

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2D natural convection flows in tilted cavities: Porous media and homogeneous fluids

Báez¹,

Nicolás²

2006

International Journal of Heat and Mass Transfer

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An operator splitting numerical scheme for thermal/isothermal incompressible viscous flows

Cited by 12 publications

References 14 publications

2D thermal/isothermal incompressible viscous flows

2D thermal/isothermal incompressible viscous flows

Unconditionally stable numerical scheme for natural convection problems

2D natural convection flows in tilted cavities: Porous media and homogeneous fluids

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