An earlier paper demonstrated a methodology for modeling the spreading process with a Gaussian random walk procedure, but was limited to the gravity-viscous spreading regime. Here we extend the methodology of representing spread and transport of oil slicks on calm sea surface by updated Voronoi diagrams to account for the surface tension-viscous spreading regime as well. We have utilized the analogy between diffusion and spreading processes by defining a step length for the particle-based random walk scheme. In this study, calculation of the diffusive length is improved by including the surface tension term in the numerical solution method. The results from the numerical simulation of the spreading oil slick agree very well with the analytical solutions. The solution is robust in that good agreement is achieved for a large range of model and numerical solution parameters. This modeling procedure remains valid only for passive, quiescent spreading. The inclusion of spreading due to important horizontal and vertical turbulent shear processes in the Voronoi diagram paradigm remains a challenge for future work.

较早的一篇论文演示了一种使用高斯随机游走程序对扩展过程进行建模的方法，但仅限于重力-粘性扩展机制。在这里，我们通过更新的Voronoi图扩展了表示在静海表面上浮油的扩散和运输的方法，从而也考虑了表面张力-粘性扩散机制。通过为基于粒子的随机游走方案定义步长，我们利用了扩散和扩散过程之间的类比。在这项研究中，通过将表面张力项包括在数值解法中，可以改善扩散长度的计算。扩散的浮油的数值模拟结果与解析解非常吻合。该解决方案的健壮性在于，可以针对各种模型和数值解决方案参数达成良好的一致性。此建模过程仅对被动静态扩展有效。Voronoi图范式中由于重要的水平和垂直湍流剪切过程而导致的扩散仍然是未来工作的挑战。