Computer simulation of web dynamics

Abstract

Explicit finite difference schemes for modeling one-dimensional, transient web dynamics are designed, developed and tested. A sequence of numerical experiments are performed to ascertain the effects of various parameters on the stability and accuracy of the numerical results. Refinement of the numerical grid led to results which converged to analytical results for stable computations. For a particular web running speed and computational duration, there exists a time-step limit for stability. Longer computational time durations as well as higher web running speeds require reduced time-step size for stable numerical results. Upstream differencing of the Coriolis term to procure stability leads to numerical damping in the computations. A combination of upstream and central differencing yields stable results at larger time-steps than that required using full central differencing as well as less damping than that produced using full upstream differencing.