Numerical simulations of the solar granulation. I - Basic equations and methods

Physics

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Computerized Simulation, Hydrodynamic Equations, Radiative Heat Transfer, Solar Granulation, Solar Physics, Continuity Equation, Convection Currents, Equations Of State, Fourier Series, Poisson Equation, Solar Atmosphere, Spectral Line Width, Spline Functions, Stellar Models

Scientific paper

Hydrodynamical and radiative transfer equations governing the evolution of granular convection patterns are discussed. The anelastic approximation of the continuity equation is used to exclude pressure waves from the problem, and numerical methods are developed to simulate the solar granulation, which are based on a two-dimensional Fourier-series representation of horizontal fluctuations, combined with a cubic spline representation in the vertical direction. The simulations are a natural representation for a medium of essentially infinite horizontal extension with strong vertical stratification, which allows a simple treatment of the viscosity-like influence ofgrid-scale motions and a rapid solution of the Poisson-type equation for the dynamic pressure, giving high numerical accuracy for a given number of mesh points.

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