Investigation of Smoothness-Increasing Accuracy-Conserving Filters for Improving Streamline Integration through Discontinuous Fields

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators-integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated, which is not available at the interelement level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by interelement discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-increasing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through a numerical example the computational trade-offs exhibited when one applies such a strategy.