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Introduction to Modeling Convection in Planets and StarsMagnetic Field, Density Stratification, Rotation$
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Gary A. Glatzmaier

Print publication date: 2013

Print ISBN-13: 9780691141725

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691141725.001.0001

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Numerical Method

Numerical Method

Chapter Two Numerical Method
Introduction to Modeling Convection in Planets and Stars

Gary A. Glatzmaier

Princeton University Press

This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. The approach involves updating for the vorticity first and then solving for the fluid velocity each time step. The chapter continues with a discussion of two very different spatial discretizations, whereby the vertical derivatives are approximated with a finite-difference method and the horizontal derivatives with a spectral method. The nonlinear terms are computed in spectral space. The chapter also considers the Adams-Bashforth time integration scheme and explains how the Poisson equation can be solved at each time step for the updated streamfunction given the updated vorticity.

Keywords:   numerical method, thermal convection, vorticity-streamfunction formulation, vorticity, fluid velocity, spatial discretization, finite-difference method, spectral method, Adams-Bashforth time integration scheme, Poisson equation

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