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"This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, Gary Glatzmaier begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a two-dimensional box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. He then describes how to implement more efficient and accurate numerical methods and more realistic geometries in two and three dimensions. In the third part of the book, Glatzmaier demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation.Featuring numerous exercises throughout, this is an ideal textbook for students and an essential resource for researchers. Describes how to create codes that simulate the internal dynamics of planets and stars Builds on basic concepts and simple methods Shows how to improve the efficiency and accuracy of the numerical methods Describes more relevant geometries and boundary conditions Demonstrates how to incorporate more sophisticated physics "--

Convection (Astrophysics) --- Planets --- Stars --- Astrophysics --- Heat --- Atmospheres of stars --- Stellar atmospheres --- Atmospheres of planets --- Planetary atmospheres --- Computer simulation. --- Mathematical models. --- Atmospheres. --- Convection --- 2.5D spherical-shell. --- 3D cartesian box. --- 3D spherical-shell. --- Adams-Bashforth time integration scheme. --- Boussinesq approximation. --- ChebyshevІourier method. --- CrankЎicolson scheme. --- Fourier expansions. --- Fourier mode. --- Fourier transforms. --- Galerkin method. --- Nusselt number. --- Poisson equation. --- Prandtl number. --- Rayleigh number. --- RayleighЂnard convection. --- Reynolds number. --- RungeЋutta scheme. --- advection. --- anelastic approximation. --- anelastic model. --- arbitrary background field. --- aspect ratio. --- boundary conditions. --- boundary layers. --- cartesian box geometry. --- computer analysis. --- computer code. --- computer graphics. --- computer simulations. --- conservation equations. --- convection. --- coordinate mapping. --- critical Rayleigh number. --- density stratification. --- diffusion. --- dispersion relation. --- double-diffusive convection. --- energy. --- entropy. --- finite-amplitude simulations. --- finite-difference method. --- fluid dynamics. --- fluid flow. --- fluid velocity. --- horizontal background field. --- infinite Prandtl number. --- internal gravity waves. --- kinetic energy spectrum. --- linear code. --- linear dispersion relation. --- linear equations. --- linear model. --- linear stability analysis. --- linear stability problem. --- magnetic field generation. --- magnetic field. --- magneto-gravity waves. --- magnetoconvection. --- magnetohydrodynamic equations. --- magnetohydrodynamics. --- mantle convection. --- marginal stability. --- mass. --- momentum. --- nonlinear code. --- nonlinear convection. --- nonlinear evolution. --- nonlinear simulations. --- nonlinear terms. --- nonuniform grid. --- numerical code. --- numerical method. --- numerical model. --- oscillating instability. --- parallel code. --- parallel processing. --- postprocessing code. --- predictor-corrector scheme. --- pressure. --- rotation. --- salt-fingering instability. --- semi-implicit scheme. --- semiconvection instability. --- spatial discretization. --- spatial resolution. --- spectral method. --- spectral space. --- spherical harmonic expansions. --- staircase profile. --- temperature profile. --- temperature. --- thermal convection. --- thermal diffusion. --- thermal stratification. --- time integration schemes. --- vorticity-streamfunction formulation. --- vorticity. --- wave energy.

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Flows of thermal origin and heat transfer problems are central in a variety of disciplines and industrial applications. The present book entitled Thermal Flows consists of a collection of studies by distinct investigators and research groups dealing with different types of flows relevant to both natural and technological contexts. Both reviews of the state-of-the-art and new theoretical, numerical and experimental investigations are presented, which illustrate the structure of these flows, their stability behavior, and the possible bifurcations to different patterns of symmetry and/or spatiotemporal regimes. Moreover, different categories of fluids are considered (liquid metals, gases, common fluids such as water and silicone oils, organic and inorganic transparent liquids, and nanofluids). This information is presented under the hope that it will serve as a new important resource for physicists, engineers and advanced students interested in the physics of non-isothermal fluid systems; fluid mechanics; environmental phenomena; meteorology; geophysics; and thermal, mechanical and materials engineering.

coating flow --- free surface --- boundary layer --- stress singularity --- matched asymptotic expansions --- computational fluid dynamics --- turbulence --- rotating thermal convection --- Rayleigh–Bénard --- heat enhancement --- nanofluid --- circular pipe --- twisted tape --- porous media --- metal foam --- convection-driven dynamos --- numerical simulations --- bistability --- mean-field magnetohydrodynamics --- spherical shells --- stochastic equations --- equivalence of measures --- nature of turbulence --- critical Reynolds number --- thermovibrational convection --- gravity modulation --- thermofluid-dynamic distortions --- patterning behavior --- stratified mixing layer --- non-modal instability --- Kelvin-Helmholtz instability --- Holmboe instability --- rotating thermal magnetoconvection --- linear onset --- sphere --- Rayleigh–Bénard convection --- time periodical cooling --- Lattice Boltzmann method --- thermocapillary-driven convection --- half-zone liquid bridges --- particles --- coherent structures --- particle accumulation structure (PAS) --- high Prandtl number fluids --- plane layer --- circular translational vibrations --- thermal vibrational convection --- convective patterns --- n/a --- Rayleigh-Bénard --- Rayleigh-Bénard convection