Jukka Tuomela

Maryam Samavaki, Jukka Tuomela

We study properties of the solutions to Navier-Stokes system on compact Riemannian manifolds. The motivation for such a formulation comes from atmospheric models as well as some thin film flows on curved surfaces. There are different choices of the diffusion operator which have been used in previous studies, and we make a few comments why the choice adopted below seems to us the correct one. This choice leads to the conclusion that Killing vector fields are essential in analyzing the qualitative properties of the flow. We give several results illustrating this and analyze also the linearized version of Navier-Stokes system which is interesting in numerical applications. Finally we consider the 2 dimensional case which has specific characteristics, and treat also the Coriolis effect which is essential in atmospheric flows.

Teijo Arponen, Samuli Piipponen, Jukka Tuomela

The purpose of this paper is to analyze the singularities of a well known benchmark problem ``Andrews' squeezing mechanism''. We show that for physically relevant parameter values this system admits singularities. The method is based on Gröbner bases computations and ideal decomposition. It is algorithmic and can thus be applied to study constraint singularities which arise in more general situations.

Jukka Tuomela, Teijo Arponen, Villesamuli Normi

We use Lagrangian formalism and jet spaces to derive a computational model to simulate multibody dynamics with holonomic constraints. Our approach avoids the traditional problems of drift-off and spurious oscillations. Hence even long simulations remain physically relevant. We illustrate our method with several numerical examples.