Cartesian Grid Euler (CGE) Solver
A perennial difficulty with volume grid-based flow solvers is the reliable generation of a good quality mesh about complex geometries. Primarily, three basic grid topologies are available: structured grids, unstructured grids and Cartesian meshes, although others such as hex and dragon meshes can also be used. Advanced grid concepts such as hybrid meshes and Chimera/Overset grids essentially derive from one or more of these basic mesh types. Structured grids employ a logically rectangular indexing structure, which allows for trivial identification of neighboring elements/faces and simple interpolation rules, and are thus highly efficient in terms of both storage and CPU. Unfortunately, structured grids are extremely difficult to generate about complex configurations and require considerable user intervention to ensure good quality (i.e., adequate resolution and minimal skewing) and proper contiguity between blocks (for multiple block structures). Unstructured meshes on the other hand, readily accommodate complicated surfaces, facilitate solution adaptation and can be generated in a nearly autonomous fashion. However, mesh generation can be expensive and care must be taken to ensure mesh quality particularly in re-entrant corners. Moreover, the resolution of the volume mesh is tightly wedded to that of the surface. The third basic mesh type is the Cartesian grid which employs the data structure known as an octree to decompose the flow domain into a collection of hierarchically nested cubes. Unlike the previous two grid constructs, the Cartesian mesh is not inherently boundary confirming. Instead, surface and volume clipping procedures are employed to explicitly deduce the necessary connectivity relations, volumes and surface areas for grid cells that intersect the body surface. The main advantage of a properly formulated Cartesian grid generation algorithm is that a mesh can be generated for virtually any closed surface or collection of surfaces.
Subsonic shuttle configurations calculated using fast panel and Cartesian grid flow analyses. M=0.5, α=10°. Overall configuration (left) and detail of flow field on aft section of fuel tank (right).
Prediction of flow around a generic civil-transport aircraft. Close-up slice through the grid (left) and streamtraces illustrating flow separation (right
To relieve the time consuming and laborious duties of mesh quality improvement for both structured and unstructured meshes, CDI developed an unsteady 3D Cartesian Grid based Euler solver (CGE) for performing routine design and analysis work. This solver exploits CDI's significant experience in octree generation and handling, polygon clipping algorithms and unstructured grid-based flow solvers. The latter being of particular importance since the data structures used to specify the cell-face and face-surface element relations closely resemble the ones employed in existing 3D unstructured grid-based flow analyses such as RSA3D. Moreover, the state-of-the art flux splitting routines, implicit time marching algorithms, higher order interpolation methods and multigrid-based acceleration schemes employed by RSA3D, in conjunction with new flow-based adaptive mesh routines, form the basis of CGE. CGE has been extensively validated for complicated geometries such as the ONERA M6 wing and the space shuttle booster combination.
Coupled CGE-VorTran-M predictions of a LPD-13 ship airwake.
Coupled CGE-VorTran-M predictions of the flow around a Ferrari 333 (left) and downtown Philadelphia, PA (right).
Recent applications of CGE to ship airwake calculations, as well as various other long-time wake problems has seen the modification of the solver to support imperfect geometries (i.e. non-watertight surface descriptions) as well as coupling to the VorTran-M module.