Adaptive energy stable artificial dissipation for preserving scalar boundedness in turbulent flows

Abstract

An adaptive dissipation scheme is developed that preserves scalar boundedness in a high-order finite difference framework satisfying the summation-by-parts (SBP) property. A sensor is introduced that switches from an SBP dissipation operator based on a high derivative order that is efficient at absorbing the highest energy modes to a second order derivative that targets energy across scales. Conditionally- and unconditionally-stable formulations are presented. Numerical experiments of a one-dimensional advection equation and a three-dimensional turbulent round jet demonstrate that scalar boundedness can be achieved within an acceptable threshold while retaining overall high-order accuracy. Although not demonstrated here, the same approach could be employed for shock capturing as well.