Marangoni–Bénard Convection with a Deformable Free Surface

Cliffe, K. A.; Tavener, Simon

doi:10.1006/jcph.1998.5995

Cited by 18 publications

(12 citation statements)

References 29 publications

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“…The benchmark-quality data on Marangoni-Bénard instability was reported in Reference [32] for heating from below. It is rather surprising that a commonly accepted benchmark problem for the thermocapillary convection in a rectangular cavity heated from the side was not formulated.…”

Section: Thermocapillary Convection Flowsmentioning

confidence: 99%

Stability of convective flows in cavities: solution of benchmark problems by a low‐order finite volume method

Gelfgat

2006

Numerical Methods in Fluids

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SUMMARYA problem of stability of steady convective flows in rectangular cavities is revisited and studied by a second-order finite volume method. The study is motivated by further applications of the finite volumebased stability solver to more complicated applied problems, which needs an estimate of convergence of critical parameters. It is shown that for low-order methods the quantitatively correct stability results for the problems considered can be obtained only on grids having more than 100 nodes in the shortest direction, and that the results of calculations using uniform grids can be significantly improved by the Richardson's extrapolation. It is shown also that grid stretching can significantly improve the convergence, however sometimes can lead to its slowdown. It is argued that due to the sparseness of the Jacobian matrix and its large dimension it can be effective to combine Arnoldi iteration with direct sparse solvers instead of traditional Krylov-subspace-based iteration techniques. The same replacement in the Newton steady-state solver also yields a robust numerical process, however, it cannot be as effective as modern preconditioned Krylov-subspace-based iterative solvers.

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Section: Thermocapillary Convection Flowsmentioning

confidence: 99%

Stability of convective flows in cavities: solution of benchmark problems by a low‐order finite volume method

Gelfgat

2006

Numerical Methods in Fluids

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“…Such an approach can also be extended to the variable density and variable viscosity cases [46], even to the case of inhomogeneous surface tension, for instance, the Marangoni-Bénard convection [22,30,37,45,52] and the case involving more complicated fluids [54].…”

Section: A Phase Field Model For the Mixture Of Two Incompressible Flmentioning

confidence: 99%

A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

Shen

2003

Physica D: Nonlinear Phenomena

573

506

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A phase field model for the mixture of two incompressible fluids is presented in this paper. The model is based on an energetic variational formulation. It consists of a Navier-Stokes system (linear momentum equation) coupled with a Cahn-Hilliard equation (phase field equation) through an extra stress term and the transport term. The extra stress represents the (phase induced) capillary effect for the mixture due to the surface tension. A Fourier-spectral method for the numerical approximation of this system is proposed and analyzed. Numerical results illustrating the robustness and versatility of the model are presented.

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“…Finally, the convergence of the velocity field (towards zero) is given in Table III. The observed quadratic convergence rate for both the pressure field and the interface location is something of a surprise, as linear convergence was observed by Cliffe and Tavener [19] using an orthogonal transformation. We suggest that the free surface location converges at one order lower than the velocity field, since the location of the free surface is essentially determined by the kinematic condition which involves derivatives of the velocity field.…”

Section: Static Meniscus Problemsmentioning

confidence: 54%

“…The contact angle is not required to be close to 90 degrees, nor is the free surface curvature required to be small. Cliffe and Tavener [19] used the finite-element method, coupled with numerical bifurcation techniques, to determine the quantitative effect of free-surface deformations on the bifurcation structure in two-dimensional single-fluid Marangoni-Bénard convection systems. For contact angles other than 90 degrees, the free surface is no longer an isothermal surface, and shear stresses exist along the free surface, arising from the temperature-dependent nature of the surface tension.…”

Section: Introductionmentioning

confidence: 99%