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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.