Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
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We compare the results of the numerical simulations of the horizontal Bridgman solidification (no-growth case) of Succinonitrile (SCN) and Silicon liquid samples. We approach several different conditions: the closed and the open top crucible in a microgravitational environment where low amplitude and low frequency g-jittering is considered. The mathematical model here adopted describes the flow of the liquid phase as an incompressible Newtonian fluid, the heat transport phenomena and the evolution of the phase front. The stream-function/vorticity formulation of the flow of the liquid phase and the front-fixing treatment of the moving phase front are used. The numerical approximation is based on a second order ENO scheme combined with a second order time scheme. Interestingly we find that, in the case of SCN, thermocapillarity induces a secondary oscillatory flow in the average Prandtl melt that is not influenced by g-jittering; furthermore, it accelerates the flow and causes the curving of the phase front. Within the Silicon sample, the low Prandtl melt does not undergo such a bifurcation and the phase front keeps flat in each case considered. In the open top crucible also the Silicon melt flow is faster than in the closed top case. In general, in the tests here considered, g-jittering appears to be uninfluencial as the only effect observed is an oscillatory behaviour of the streamfunction characterized by the same amplitude and frequency.