Tham khảo tài liệu 'applied computational fluid dynamics techniques - wiley episode 1 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | GRID GENERATION 61 D1. Assume given a boundary point distribution. D2. Generate a Delaunay triangulation of the boundary points. D3. Using the information stored on the background grid and the sources compute the desired element size and shape for the points of the current mesh. D5. nnewp 0 Initialize new point counter D6. do ielem 1 nelem Loop over the elements Define a new point inewp at the centroid of ielem Compute the distances dispc 1 4 from inewp to the four nodes of ielem Compare dispc 1 4 to the desired element size and shape If any of the dispc 1 4 is smaller than a fraction a of the desired element length skip the element goto D6 Compute the distances dispn 1 nneip from inewp to the new points in the neighbourhood If any of the dispn 1 nneip is smaller than a fraction P of the desired element length skip the element goto D6 nnewp nnewp 1 Update new point list Store the desired element size and shape for the new point enddo D7. if then Perform a Delaunay triangulation for the new points goto endif The procedure outlined above introduces new points in the elements. One can also introduce them at edges George and Borouchaki 1998 . In the following individual aspects of the general algorithm outlined above are treated in more detail. . CIRCUMSPHERE CALCULATIONS The most important ingredient of the Delaunay generator is a reliable and fast algorithm for checking whether the circumsphere -circle of a tetrahedron triangle contains the points to be inserted. A point Xp lies within the radius Ri of the sphere centred at Xc if dp Xp - Xc Xp - Xc Rp. This check can be performed without any problems unless dp - Ri 2 is of the order of the round-off of the computer. In such a case an error may occur leading to an incorrect rejection or acceptance of a point. Once an error of this kind has occurred it is very difficult to correct and the triangulation process breaks down. Baker 1987 has determined the following condition Given the set of .
