Abstract
A method for improving the accuracy of hydrodynamical codes that use a moving
Voronoi mesh is described. Our scheme is based on a new regularization scheme
that constrains the mesh to be centroidal to high precision while still
allowing the cells to move approximately with the local fluid velocity, thereby
retaining the quasi-Lagrangian nature of the approach. Our regularization
technique significantly reduces mesh noise that is attributed to changes in
mesh topology and deviations from mesh regularity. We demonstrate the
advantages of our method on various test problems, and note in particular
improvements obtained in handling shear instabilities, mixing, and in angular
momentum conservation. Calculations of adiabatic jets in which shear excites
Kelvin Helmholtz instability show reduction of mesh noise and entropy
generation. In contrast, simulations of the collapse and formation of an
isolated disc galaxy are nearly unaffected, showing that numerical errors due
to the choice of regularization do not impact the outcome in this case.
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