John C. Chien

January 5, 1999 11:09 
Re: unstructured vs. structured grids
Good questions! I would say that it depends on (1) the complexity of the problem you are trying to solve, and (2) the code you are trying to use. To be fair, you should use the same code to solve the problem using both the structured mesh and the unstructured mesh. Also you should use the same code to grid the simple problem and the complex problem. To answer your second question first. For simple problem, say a single block problem, the gridding time would be about the same. In both cases, you have to create the geometry, including points, curves, and surfaces. It's not too bad for a single block of geometry, 8 curves, 6 surfaces. After the nodal points are distributed, the surface mesh and the volume mesh can be easily done using algebraic method for both the structured and unstructured meshes. For complex multiblock problems, based on my experience, the most time consuming part is to create the geometry itself. This step can take several days to several weeks. The time spend in actual mesh generation is relatively small. You generate the surface mesh first, and then generate the volume mesh next. Here. the biggest problem is: if the geometry is not properly modelled, most of the time, the automatic unstructured mesh generator will have hard time to complete the meshing operation. It's hard to generate hundred of thousands mesh points automatically for any arbitrary geometry ( geometry model). In this case, the structured mesh ( multiblock) generation should be more reliable in generating a final mesh because the mesh generation inside the block has been worked out in advance. The same reliability applies to the multiblock unstructured mesh generation approach. In most cases, unstructured mesh code are not multiblocked. This increases the failure rate. So, in the complex geometry problem, you are forced to modify the geometry model in order to get a successful unstructured volume mesh. For complex geometry problems, you will be spending a lot of time modifying the geometry model in order to generate a volume mesh regardless of the methods used, structured or unstructured. And even after the mesh is generated, the refinement of the mesh will continue till the problem is finally solved. ( remember that a poor mesh will give you a poor answer, and sometimes a diverged or oscillating solutions). To answer the first question: assuming that the code save every temporary variable and arrays to save the computing time, then the solution time should be the same. It takes more time to solve when you have more cell volumes to solve. ( many volumes share a common grid point). In 2D, structured triangular mesh has twice the cell numbers as the structured rectangular mesh. In other words, you need one extra point to grow a triangular cell, and it takes two extra points to create a new rectangular cell. Overall, 2D problems are not sensitive to the methods used because the geometry is easy to see and easy to control. the computing time is not critical and normally is proportional to the total number of cells. ( structured mesh method can sometimes more efficient if linerelaxation or the like is used.) For complex geometry problems, there is no easy answer to the meshing problem yet. You may be spending a lot of time just trying to find a successful unstructured mesh , automatically.( it is not practucal to edit a 3d unstructured mesh. ) So, how to generate a good 3D mesh for complex geometry problem is still largely unsolved.( a good mesh is the one which gives good solution.)
