Title: Analytical benchmark solution for Stokes flow with variable viscosity in spherical layer

Authors: Igor Y. Popov; Ilya Makeev; Irina V. Blinova

Addresses: ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia ' ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia ' ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia

Abstract: Stokes flow with variable viscosity in a spherical layer is considered. This task appears in many geophysical problems related to mantle convection. For a particular case of spherically symmetric viscosity and density distributions, a solution of the system of the Stokes and continuity equations is constructed in an analytic form. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Finite difference scheme for multigrid algorithm for solving Stokes equations with variable viscosity in a spherical coordinate system has been derived. Scheme has been tested by comparing with benchmark solutions.

Keywords: Stokes flow; benchmark solution; multigrid method.

DOI: 10.1504/PCFD.2018.089501

Progress in Computational Fluid Dynamics, An International Journal, 2018 Vol.18 No.1, pp.56 - 68

Published online: 29 Jan 2018 *

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