A Single Stage Flux-Corrected Transport Algorithm for High-Order Finite-Volume Methods
This work addresses the need for efficient and accurate limiters in high-order finite-volume methods for advection problems, but it is an incremental improvement over existing flux-corrected transport algorithms.
The authors present a new limiter method for solving the advection equation using high-order finite-volume methods, based on flux-corrected transport. The method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions, requiring only one limiter application per time step.
We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the pre-constraint on the high-order fluxes. We compute the high-order fluxes via a method of lines approach with fourth order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.