The Application of Multiple One-Dimensional Adaptive Grid Method

Revisit to the Modified Multiple One-Dimensional Adaptive Grid Method

“…(8) becomes (10) If a third cycle is applied, the (b l + b 2 ) term is replaced by tb, Since the multiple one-dimensional adaptive procedure's damping comes from the weight function, the final grid system cannot be free from grid oscillation except for a relatively small adaptive factor. Fortunately, a careful examination of all the test cases in [13][14][15][16][17][18][19][20] reveals that the long-wave oscillations of the grid distribution have no major impact on the accuracy of the final solutions. In order to eliminate the short -wave grid oscillation and simultaneously preserve the grid adaptation, the following grid smoothing method is employed: (11) ( t:.st + t:.sj )…”

“…However, Jeng and co-workers [16,17] pointed out that this multiple onedimensional scheme may cause excessive grid skewness and proposed a modified weight function. For example, the weight function of a point along an~= constant line takes the form [16] W(S)=I+b{A 1IBTI +O_A1_Az)IBT, +Az\BTI } for interior lines ss U-I Bs U Bs U+I W(s) = 1 + b{O -Az)1 BT I + Azi BT I } ss U ss U+ I for boundary lines (5) In [17] the averaging is extended to include several grid lines whose j = constant. Lee and Tsuei [18] further extended the averaging region and modified the weighting function for a (j, k) point:…”

“…1. In the second cycle of the adaptive procedure, either the method of [18] or the modified method combining methods of [18] and [16,17] can be applied to improve solution accuracy. 2.…”

“…Since the adaptive procedure along every grid line is independent of the other grid lines, excess grid skewness might exist around an isolated high-gradient region. Jeng and co-workers [16,17] modified the weighting function of the one-dimensional adaptive grid procedure by coupling information from adjacent grid lines, thereby improving grid skewness to a certain extent. Lee and Tsuei [18] further included the information along the line of grid adaptation to the coupling and successively developed their hybrid adaptive grid scheme [19,20].…”