A Space-Time Approach to Nonlinearly Stable Flux Reconstruction

Efficient and robust high-order methods are imperative for developing computational fluid dynamics methods with genuine predictive capacity. To this end, we propose a novel space-time flux reconstruction approach which is fully-discretely entropy-stable for the discontinuous Galerkin correction function. By using discontinuous polynomial bases in time, the method herein applies favourable features of high-order schemes to the temporal discretization, such as the capacity to perform hp-adaptation. We present the scheme's construction and verify high-order convergence using linear advection and Euler test cases, and demonstrate that using flux reconstruction reduces cost to about 70% of the uncorrected equivalent by improving the convergence of the implicit solve.