Investigation and mitigation of dispersion errors in a Navier-Stokes solver with variable resolution

Details

Supervisors

Winckelmans, Grégoire

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

Using a self-written 2D Navier-Stokes finite difference solver with variable resolution, we will analyze errors resulting from mesh coarsening. This work will focus on the often overlooked dispersion errors that occur when complex vortex structures are convected from a region of high resolution (grid size small enough to properly capture the physics) to a region of too low resolution (grid size too large to capture the physics involved). The first part concerns the investigation of the errors. This is done on a benchmark problem, a case of two counter-rotating Gaussian vortices in a periodic box. This case is interesting because analytical results exist and because the induced velocity is sufficient to convect the vortex dipole into the variable resolution. A more complex scenario is then explored by adding two secondary vortices to the primary setup, creating a four-vortex system with interactions between the vortices. The second part of this work concerns an error reduction strategy originally developed for commutation errors in LES solvers. This reduction term is based on a high order derivative, also called hyperdiffusion, with a coefficient that depends on the variation of the space step size. We will apply this to our DNS case and aim to ensure that oscillations due to dispersion errors are not backscattered, but rather dissipated in an appropriate way.