Accurate and efficient Jones-Worland spectral transforms for planetary applications
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Date
2021-07
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Conference Paper
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yes
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Abstract
Spectral transforms between physical space and spectral space are needed for fluid dynamical calculations in the whole sphere, representative of a planetary core. In order to construct a representation that is everywhere smooth, regular and differentiable, special polynomials called Jones-Worland polynomials, based on a type of Jacobi polynomial, are used for the radial expansion, coupled to spherical harmonics in angular variables. We present an exact, efficient transform that is partly based on the FFT and which remains accurate in finite precision. Application is to high-resolution solutions of the Navier-Stokes equation, possibly coupled to the heat transfer and induction equations. Expected implementations would be in simulations with P3 degrees of freedom, where P may be greater than 103. Memory use remains modest at high spatial resolution, indeed typically P times lower than competing algorithms based on quadrature.
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published
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Book title
PASC '21: Proceedings of the Platform for Advanced Scientific Computing Conference
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Pages / Article No.
16
Publisher
Association for Computing Machinery
Event
Platform for Advanced Scientific Computing Conference (PASC 2021)
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Subject
Spectral method; Computational fluid dynamics; HPC
Organisational unit
03734 - Jackson, Andrew / Jackson, Andrew
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Funding
833848 - Unravelling Earth’s magnetic history and processes UEMHP (EC)
165641 - Understanding planetary magnetic fields from theoretical, numerical and analogue models (SNF)
165641 - Understanding planetary magnetic fields from theoretical, numerical and analogue models (SNF)
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