An explicit, positivity-preserving flux-corrected transport scheme for the transport equation using continuous finite elements

Entropy viscosity, in conjunction with flux-corrected transport (FCT), is applied to a Pi continuous finite element (CFEM) discretization of the time-dependent transport equation to produce a positivity-preserving scheme that satisfies a local discrete maximum principle. Fully explicit time discretizations are employed, including explicit Euler and strong-stability-preserving Runge-Kutta (SSPRK) schemes such as the 3-stage, 3rd-order-accurate Shu-Osher scheme (SSPRK33). These explicit time discretizations require that a CFL condition be satisfied, making many practical simulations prohibitively expensive; however, this research is intended to be extended to implicit time discretizations and steady-state simulations, where CFL conditions do not apply. Results are presented for 1-D test problems.