Analysis of Error in Interpolation-Based Pathline Tracing

Chandler et al. [COJ15] presented interpolation-based pathline tracing as an alternative to numerical integration for advecting tracers in particle-based flow fields and showed that their method has lower error than a numerical integration-based method for particle tracing. We seek to understand the sources of the error in interpolation-based pathline tracing. We present a formal analysis of the theoretical bound on the error when advecting pathlines using this method. We characterize the error experimentally using characteristics of the flow field such as neighborhood change, flow divergence, and trajectory length. Understanding the sources of error in an advection method is important to know where there may be uncertainty in the resulting analysis. We find that for interpolation-based pathline tracing the error is closely related to the divergence in the flow field.