A vorticity confinement correction for discontinuous Galerkin schemes applied to fluid flow problems

Purpose Vortices are ubiquitous in fluid flows, yet accurately preserving their dynamics in numerical simulations over extended timescales and distances remains challenging. Discretisation schemes often introduce artificial dissipation exceeding physical viscosity, flattening vortical structures and disrupting their delicate dynamics. This paper aims to introduce a vorticity confinement correction for discontinuous Galerkin discretisation methods, designed to enhance the fidelity of direct numerical simulations of unsteady, vortex-dominated flows at arbitrarily high orders of accuracy. Design/methodology/approach This approach builds upon the classical VC2 correction for finite volume schemes, incorporating an additional volumetric correction specific to the discontinuous Galerkin discretisation. Findings This paper shows through an isentropic vortex transport problem that the vorticity confinement correction substantially improves vorticity conservation, evaluated here at second- and third-order spatial accuracies. This paper further demonstrates a significant gain in preserving both large and small vortices in three-dimensional transitional turbulence at second-order spatial accuracy. Originality/value To the best of the authors’ knowledge, this is the first time a Vorticity Confinement method is developed and evaluated in the context of discontinuous Galerkin schemes.