Pressure-velocity coupling on unstructured collocated grids: reconciling stability and energy-conservation

Abstract

In this work, an energy-preserving unconditionally stable fractional step method on collocated unstructured grids is presented. Its formulation is based on preserving the underlying symmetries of the differential operators. This formulation was proven to be unconditionally stable even for highly distorted meshes [1, 2]. Conservation of (global) kinetic energy is also a key feature in simulations. Within this context, a canonical case is tested, a differentially heated cavity, in order to show that the (artificial) kinetic energy error introduced by the pressure is negative and small compared with the physical dissipation. Furthermore, a stability and accuracy comparison is done for the three classical ways of interpolating the pressure gradient: linear interpolation, mid-point interpolation and volumetric interpolation.