Spectral variational approach to the non-Newtonian stokes problem in a spherical shell
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Cited by (12)
SHAVEL: A program for the spherical harmonic analysis of a horizontal vector field sampled in an equiangular grid on a sphere
2018, Computer Physics CommunicationsCitation Excerpt :Common examples are the vector spherical analyses of the Earth’s lithospheric magnetization [1], the Earth’s crustal deformation [2], the global atmospheric wind field [3], the local field of stellar tangential velocities [4,5], the astrometric catalogues [6] and the ocean flow velocities [7 ]. Complementary, the vector spherical harmonic representation of vector fields is employed to solve partial differential equations, e.g., fluid mechanics equations [8], geomagnetic dynamo [9,10], the Navier–Stokes equation of motion [11,12] and the magnetic induction equation [13]. There are, at least, two methods that can be used for the spherical harmonic analysis of vector measurements performed on a sphere.
Local well-posedness for Boussinesq approximation with shear dependent viscosities in 3D
2016, Computers and Mathematics with ApplicationsOverview of adaptive finite element analysis in computational geodynamics
2013, Journal of GeodynamicsCitation Excerpt :Many of the earliest three-dimensional mantle convection simulations utilised spectral methods (e.g., Young, 1974; Glatzmaier, 1988; Bercovici et al., 1989; Tackley et al., 1993; Zhang and Christensen, 1993; Zhang and Yuen, 1995; Machetel et al., 1995; Harder and Christensen, 1996). Such methods are especially attractive for problems involving constant viscosity or radial viscosity profiles, however the inclusion of a laterally varying viscosity structure significantly complicates the methodology and increases the computational cost (e.g., Christensen and Harder, 1991; Čadek et al., 1992; Zhang and Christensen, 1993; Forte and Peltier, 1994; Tromp and Mitrovica, 1999). The first three-dimensional, spherical model of mantle convection simulations was presented by Baumgardner (1985) using the code Terra.
The stokes problem with 3D Newtonian rheology in a spherical shell
1993, Computer Physics CommunicationsCoupling mantle convection and tidal dissipation: Applications to Enceladus and Earth-like planets
2010, Journal of Geophysical Research: PlanetsThe periodic initial value problem and initial value problem for the non-newtonian Boussinesq Approximation
2003, International Journal of Phytoremediation