Manipulating boundaries and viscous regions of unstructured meshes using Winslow's equations

The Winslow elliptic smoothing equations have been shown to be effective for smoothing both structured and unstructured meshes. Previous work has shown that it is not necessary for the computational space of an unstructured mesh to be constructed as an overarching system but that each node in computational space can be treated as having an individual virtual control volume. Using virtual control volumes, the Winslow equations have been shown to be ideal for smoothing nonboundary nodes in inviscid regions but of limited use in other situations. Modifications to the implementation of virtual control volumes are presented that allow the Winslow equations to be applied to regions to which they would otherwise not be well suited. By introducing ghost points to complete the computational space stencil for boundary points, the Winslow equations can be applied to boundary nodes, which traditionally have been held static, whereas interior mesh points are smoothed. By modifying the computational space virtual control volumes such that the central node is offset from the center of its isotropic position, the Winslow equations can be applied to highly anisotropic viscous regions of unstructured meshes.