Validity test of a Stokes flow solver by fluid rope coiling: Toward plate-mantle simulation

In this study, we propose a so-called fluid rope coiling to use as a validity test of our simulation scheme designed to solve the plate-mantle problem in the Eulerian frame of reference. In a plate-mantle unified system, a subducting plate is known to show various large and complex deformations. A numerical simulation for the plate-mantle problem is required to solve such plate motions properly without serious numerical errors. Fluid rope coiling, in which a coiling motion of viscous fluid is poured onto a horizontal plane from a certain height with the shape of a thin rope, is known to be one such motion. We reproduced the coiling rope of a Stokes flow by two different methods: a three-dimensional simulation and simplified one-dimensional solution. Quantitative comparison of these methods enables us to evaluate the accuracy of the simulation scheme for large non-linear deformation problems.