M. Behr, Rice MEMS - Shear-Slip Mesh Update Method

Modeling of Spinning and Translating Geometries

Figure 5: Flow around a propeller: Pressure field on the propeller surface and single iso-surface.

Figure 6: Flow around a propeller: Helicity field on the propeller surface and single iso-surface.

Another application of the stabilized space-time formulation has been found in modeling of geometries which undergo large regular deformations, such as rotations or translations of their individual elements. Only simplest cases in this category can be modeled by adjusting the frame of reference. When the motion of the elements is with respect to each other, that simple approach fails. Another way of handling these problems is to adjust the interior mesh as described in the previous section and then remesh. Remeshing, defined as creating new finite element mesh with a new connectivity, necessitates projection of the old solution onto the new mesh, which generally results in smearing of features of the solution. However, with the use of custom designed meshes, certain motions of the domain boundaries can be accommodated by repetitive deformation of elements within the time step, followed by frequent regeneration of element connectivity. The goal of the special mesh design is the matching of the node positions of the old (deformed) and the new (good-quality) meshes, so that projection is not necessary. In the case of rotation of an internal component, the object is surrounded by a disc of rigid mesh rotating with the component. This disc is in turn surrounded by stationary mesh spanning the external non-moving boundaries. Between the two subdomains, one can place a layer of elements which deform to absorb the motion of the internal disc, and then reconnect to new nodes on the surface of that disc, providing a mesh of the same quality as the original one. Figure 5 shows, at an instant during the simulation, the pressure field on the surface and in the vicinity of a propeller, which is immersed in a high-Reynolds number uniform flow. Figure 6 shows the corresponding helicity patterns. The layer of deforming elements is unnoticeable in the solution, and significant thrust is being generated in this simulation. Application of this methodology may include studies of flow interaction between a helicopter rotor or a submarine propeller, and fuselage and hull, respectively.

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