A Second-Order Advection-Reflection Solver

Zehnder et al. [2018] recently introduced an advection-reflection method for fluid simulation that dramatically reduces artificial dissipation. We establish a connection between their method and the implicit midpoint time integration scheme, and present a simple modification to obtain an advection-reflection scheme with second-order accuracy in time. We compare with existing alternatives, including a second-order semi-Lagrangian method based on BDF2, and demonstrate the improved energy-preservation properties.