Mathematical Sciences: Convergence of Vortex Methods

如果粘性的影响可以忽略，则不可压缩流体的流动可以用涡旋法来近似。如果流体是粘性的，则可以用随机旋涡方法来近似。本研究程序利用这些方法来研究近似解的收敛问题。了解它们的汇聚点将使这些方法变得可靠，因此也很有用。对收敛速度的了解将使我们能够在效率和成本方面与其他方法进行比较。

The flow of an incompressible fluid can be approximated by the vortex method if effects of viscosity are negligible. It can be approximated by the random vortex method if the fluid is viscous. This research program investigates the convergence of the approximate solutions by these methods. Knowing that they converge will make these methods reliable and therefore useful. Knowledge on the rate of convergence will allow comparisons with other methods in efficieny and cost.