Effects of Physical Coordinate Clustering on Boundary Vorticity Approximations in von Mises Coordinates

Abstract

Forward finite difference expressions of first-order accuracy for boundary vorticity on a solid boundary are evaluated in this work when the physical coordinates are clustered and mapped using von Mises coordinates. Results show that schemes using in-field grid points do not improve solutions obtained. Results also show that the finer the grid used in the physical domain, and the more clustered it is, improves the boundary vorticity values in the computational domain. The “best” expressions forward finite difference expressions are identified when two, three, four and five grid points are used.