A new trajectory integration scheme in the semi-lagrangian framework

In the typical semi-Lagrangian framework for Navier-Stokes equations, the advection source positions for each grid center points are repeatedly estimated to get interpolated physical quantities. Most research efforts are concentrated on the numerical accuracy, especially for the interpolation of target physical quantities. In this paper, we adopted an improved trajectory integration scheme during the advection calculation process. Our method traces the grid center points using their previous velocities at the previous time step, while other previous methods use their current velocities. Our experimental results show remarkable improvements, and we achieved real-time processing capability even with straight-forward serial implementations.