Development of a Three Dimensional Compressible Flow Solver with Hybrid Elements

Development of a Three Dimensional Compressible Flow Solver with Hybrid Elements

Weiyang Lin, Kidambi Sreenivas

The implementation of a 3D flow solver with hybrid elements has raised the complexity of dealing with meshes. Typical elements used in three dimensions include tetrahedron, pyramid, prism, and hexahedron. While most of the formulations are similar to its 2D counterpart (see 2D inviscid flow solver), the construct of hash tables such as element-to-point map, point-to-point map, and edge-to-node map, and element-to-element map involves appropriate treatments on elements:

Because of the sparsity of the flux Jacobian matrix, the nodes are typically re-ordered using a Cuthill-Mckee algorithm to reduce the effective band width:

The details will be updated in the future. The flow solver is run on a coarse and a fine mesh with a ramp shape:

A simulation video is shown below: