On the Use of Temporal Reachout Technique for Characteristics Method with Time-Line Cubic Spline Interpolation

The study had indicated that the computational performances of the characteristics method with the time-line cubic spline interpolation are related to the endpoint constraint, especially for large Courant number in which the foot of the characteristic trajectory is located near the endpoint. The first derivative endpoint constraint with higher-order central difference approximation provides better simulation results among various endpoint constraints, but it still induces some degree of numerical error. In this study, by locating the foot of the characteristic trajectory away from the endpoint, the temporal reachout technique is proposed to avoid the effect of endpoint constraint on the time-line cubic spline interpolation. Modeling the transport of a Gaussian concentration distribution in a uniform flow with constant diffusion coefficient and the viscous Burgers equation is used to examine the temporal reachout technique. The outcomes show that the temporal reachout technique yields much better simulation results than the first derivative endpoint constraint with higher-order central difference approximation. The effect of endpoint constraint on the time-line cubic spline interpolation can be greatly diminished by the use of the temporal reachout technique.