Conservative correction procedures utilizing artificial dissipation operators

Abstract

The conservative correction procedure of Abgrall [1] is studied from the perspective of filter-based artificial dissipation methods, which motivates the ability to tailor the behavior of the method in both physical and spectral space. Compared to the original formulation, employing diffusion operators biases the correction towards smaller scales and better controls discretization errors when seeking to enforce auxiliary conservation relations. Effective entropy-stable regularization of sharp gradients is furthermore shown to be attainable. Calculations of the Sod shock tube problem as governed by the one-dimensional Euler equations are used to highlight the utility of considering alternate filters within the original correction framework, where the notion of entropy conservation/stability is leveraged for improving non-linear scheme robustness.