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  • 1
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    Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime (1991)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 3; 2105-211
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  • 2
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    Simulation of particle mixing by turbulent convective flows on the connection machine (1992)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: Mixing of particles by chaotic flow fields was simulated on the Connection Machine. Each cell was assigned to the processor, and the coordinates of particles residing on the cell were kept in the local memory of the processor. This approach implies the exchange between the local memories, when a particle moves from one cell to another. Approximately 10 exp 5 particles were injected into a time-dependent flow field obtained by solving the nonlinear system of partial differential equations describing turbulent thermal convection. The flow field was calculated on a CRAY, and data were transferred to a CM-200 through a high-speed HIPPI channel.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Supercomputing '92; Proceedings of the Conference, Minneapolis, MN, Nov. 16-20, 1992 (A94-10682 01-62); p. 294-300.
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  • 3
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    Plume structures in the hard-turbulent regime of three-dimensional infinite Prandtl number convection (1993)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: Numerical simulations of three-dimensional infinite Prandtl number thermal convection with Rayleigh number (Ra) up to 10 exp 8 are reported. Convection with Ra higher than 10 exp 7 is characterized by the appearance of disconnected thermal plumes. The smaller plumes are detached by the currents produced by the larger plumes. The low wavenumber portion of a thermal power spectrum near the boundary layer becomes flat at high Ra, while the spectrum measured in the interior shows a positive slope for low wavenumbers. Differences are found in the thermal spectra between 2D and 3D models.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Geophysical Research Letters (ISSN 0094-8276); 20; 5; p. 383-386.
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  • 4
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    Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties (1994)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 113; 1; p. 62-74
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