Conservation of Angular Momentum in the Navier-Stokes equations using the Mimetic Spectral Element Method
J.D. Koning (TU Delft - Aerospace Engineering)
M.I. Gerritsma – Mentor (TU Delft - Aerospace Engineering)
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Abstract
The mimetic spectral element method is a new but powerful method for the discretisation of partial differential equations. This new method has been successfully used for computational fluid flow problems and has shown a promising ability to strictly conserve quantities. In this work the mimetic spectral element method is explored with the intent to exactly conserve angular momentum in a fluid flow. In order to achieve the exact conservation of angular momentum on general grids a formulation using mixed basis on differential forms and transformations to curvilinear grids is posed for the stokes equations. This formulation is then evolved in time by semi-discretisation and in space by a Lagrangian moving mesh method to represent a simulation of the Navier-Stokes equations.