Three-dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

“…The resulting scheme corresponds to the one proposed in Ref. [56] by Braaten and Connell for tetrahedral grids (see Ref. [43] for more details).…”

“…It can suffer from oscillations as will be shown later. Braaten and Connell [56] take the common approach as well, but their scheme does not suffer. Their success appears due to the use of the Green-Gauss gradient (instead of the least-squares gradient) which cancels the damping term even if formulated so as to ensure high-frequency damping as above.…”

Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

“…Webster et al [20] developed an adaptive ÿnite-element methodology, in which the ÿnite quadtree mesh generator, interpolation-based error indicator and edge-based mesh enrichment procedure were employed. On a fully unstructured mesh of tetrahedral elements, a solution adaptive multigrid scheme [21] was developed to study the transonic ows about an aircraft engine nacelle. A general adaptation procedure [22] based on h-reÿnement and coarsening was developed to improve the resolution of complex ow features.…”

Incompressible Navier–Stokes method with general hybrid meshes

“…This edge-dual approach has been advocated by other researchers [3,27] because it is less susceptible to the solution wiggles and yields more compact stencils than other methods. However, visiting edge-duals and performing surface integrals over various kinds of edge-duals introduces extra complexity.…”