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DTSTAMP:20210916T132446Z
LOCATION:Mère Royaume
DTSTART;TZID=Europe/Stockholm:20210705T133000
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UID:submissions.pasc-conference.org_PASC21_sess213_pap113@linklings.com
SUMMARY:Accurate and Efficient Jones-Worland Spectral Transforms for Plane
 tary Applications
DESCRIPTION:Paper\n\nAccurate and Efficient Jones-Worland Spectral Transfo
 rms for Planetary Applications\n\nMarti, Jackson\n\nSpectral transforms be
 tween physical space and spectral space are needed for fluid dynamical cal
 culations in the whole sphere, representative of a planetary core. In orde
 r to construct a representation that is everywhere smooth, regular and dif
 ferentiable, special polynomials called Jones-Worland polynomials, based o
 n a type of Jacobi polynomials, are used for the radial expansion, coupled
  to spherical harmonics in angular variables. We present an exact, efficie
 nt transform that is partly based on the FFT and which remains accurate in
  finite precision. Application is to high-resolution solutions of the Navi
 er-Stokes equation, possibly coupled to the heat transfer and induction eq
 uations. Expected implementations would be in simulations with $P^3$ degre
 es of freedom, where $P$ may be greater than $10^3$. Memory use remains mo
 dest at high spatial resolution, indeed typically $P$ times lower than com
 peting algorithms based on quadrature.\n\nDomain: CS and Math
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