Analytical solution for viscous incompressible Stokes flow in a spherical shell
Keyword(s):
Abstract. I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial and of power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g. the root mean square velocity, are analytically computed. This forms the basis for a numerical benchmark for convection codes and I have implemented it in two finite element codes ASPECT and ELEFANT. I report on error convergence rates for velocity and pressure.
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2019 ◽
Vol 219
(3)
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pp. 1915-1938
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2019 ◽
Vol 217
(1)
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pp. 650-667
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2019 ◽
Vol 356
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pp. 175-198
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2011 ◽
Vol 69
(3)
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pp. 534-549
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2014 ◽
Vol 24
(08)
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pp. 1495-1539
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2019 ◽
Vol 347
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pp. 568-587
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