Radek Pecher¹, Steve Elston, Peter Raynes

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 91-102, 2006, DOI:10.3970/cmes.2006.013.091

Abstract Meshfree techniques for solving partial differential equations in physics and engineering are a powerful new alternative to the traditional mesh-based techniques, such as the finite difference method or the finite element method. The elimination of the domain mesh enables, among other benefits, more efficient solutions of nonlinear and multi-scale problems. One particular example of these kinds of problems is a Q-tensor based model of nematic liquid crystals involving topological defects.
This paper presents the first application of the meshless local Petrov-Galerkin method to solving the Q-tensor equations of nematostatics. The theoretical part introduces the Landau More >

V.G. Kozlov¹, N.V. Selin²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.2, pp. 107-118, 2006, DOI:10.3970/fdmp.2006.002.107

Abstract Thermal vibrational convection in a sector of a thin spherical liquid layer subjected to pendulum vibrations (spherical pendulum) is investigated theoretically and experimentally. Temperature non-uniformity inside the liquid is caused by uniformly distributed internal heat sources (one side of the layer is isothermal, the other one is adiabatic). Experiments are carried out under conditions of stable temperature stratification in the gravity field. Heat transfer and convective structure are investigated in a wide interval of governing dimensionless parameters. A critical increase of heat transfer is revealed as the vibrations intensity is increased, caused by average convection. More >

K. Matsunaga¹, H. Kawamura¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 59-64, 2006, DOI:10.3970/fdmp.2006.002.059

Abstract Existing studies on solidification phenomena mainly focused on the solidification processes per se. In real systems, however, one cannot neglect the effects of molten material convective flow, such as natural and thermocapillary convection (they strongly affect the resulting quality of the solidified materials). The present study aims to experimentally investigate on the effect of the thermocapillary flow upon the directional solidification in a liquid layer with a free upper surface. If no free surface exists, the solid--liquid interface (SLI) is vertical and straight, while, with the free surface, the SLI is inclined against the wall-normal More >

M.El-Gammal¹, J.M.Floryan¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 17-26, 2006, DOI:10.3970/fdmp.2006.002.017

Abstract Interface deformation and thermocapillary rupture in a cavity with free upper surface subject to concentrated heating from above is investigated. The dynamics of the process is modulated by placing different amounts of liquid in the cavity. The results determined for large Biot and zero Marangoni numbers show the existence of limit points beyond which steady, continuous interface cannot exist and processes leading to the interface rupture develop. Evolution of the limit point as a function of the mass of the liquid is investigated. The topology of the flow field is found to be qualitatively similar, More >

B.B. Karki¹, D. Bhattarai¹, L. Stixrude²

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 107-118, 2006, DOI:10.3970/cmc.2006.003.107

Abstract Computer modeling of liquid phase poses tremendous challenge: It requires a relatively large simulation size, long simulation time and accurate interatomic interaction and as such, it produces massive amounts of data. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase. This paper reports the details of methodology used in the context of liquid simulations and subsequent analysis of the output data. For illustration purpose, we consider the results for the liquid phases of two geophysically relevant materials, namely MgO and MgSiO₃. The simulations are performed using the parallel first-principles More >

D. E. Melnikov¹, V. M. Shevtsova²

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 189-200, 2005, DOI:10.3970/fdmp.2005.001.189

Abstract Buoyancy-driven convective flows are numerically analyzed in a cubic enclosure, containing a liquid subjected to a temperature difference between opposite lateral walls; all other walls are thermally insulated. The stationary gravity vector is perpendicular to the applied temperature gradient. The steady flow patterns are investigated within the framework of a liquid particles tracing technique. Three tracing techniques are compared: the first, based on a trilinear interpolation of the liquid velocity defined on the computational grid and an eighth order in time Runge-Kutta method; the second and the third, using a resampling the velocity field on… More >