A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere

摘要: Abstract We present a fully spectral methodology for magnetohydrodynamic (MHD) calculations in whole sphere. The use of Jones–Worland polynomials the radial expansion guarantees that physical variables remain infinitely differentiable throughout spherical volume. Furthermore, we mathematically motivated and systematic strategy to relax very stringent time step constraint is close origin when harmonic used angular direction. new allows significant savings even on relatively simple solutions as demonstrated so-called full sphere benchmark, specific problem with accurately-known solution. numerical implementation uses 2D data decomposition which it scale thousands cores present-day high performance computing systems. In addition validation results, also three dynamo structure.