### Table 23: blkdat.input - Model Input Parameters

2003

"... In PAGE 73: ...26 APPENDIX B Table23 : blkdat.input - Model Input Parameters Parameter Description slip = +1 for free-slip, -1 for non-slip boundary conditions.... In PAGE 74: ...blkdat.input Model Input Parameters 69 Table23 : blkdat.input - Model Input Parameters Parameter Description niter KPP: Iterations for semi-implicit solution.... ..."

### Table 2. Boundary Conditions for

"... In PAGE 11: ... Boundary conditions for the n expansion coe cients are required. Consistent with the boundary conditions for the tensor function f ij , the corresponding n bound- ary conditions are listed in Table2 as functions of ij (see Appendix A for details). The equivalence of the elliptic relaxation of the expansion coe cients n given by Eq.... ..."

### Table 1: Boundary conditions

in SUMMARY

"... In PAGE 5: ... The narrowness of the Gaussian pro#0Cle has a relevant in#0Duence on the calculated #0Dame length, so that its parameters have to be determined appropriately #5B19#5D. The boundary conditions are summarized in Table1 . Finally, we note that the use of the de#0Cnition of the vorticity #281#29 for the vorticity outlet boundary condition does not yield any relevantchanges in the computed solution.... In PAGE 5: ... 3. GENERAL SOLUTION ALGORITHM The partial di#0Berential equations #282#29 together with the boundary conditions #28see Table1 #29 are discretized on a two dimensional tensor product grid. A solution is #0Crst obtained on an initial coarse grid.... In PAGE 6: ...i#0Berence expressions. Di#0Busion and source terms are evaluated using centered di#0Berences. We adopt a monotonicity preserving upwind scheme for the convective terms #28see #5B20, p. 304#5D#29, for instance, v r @S @r = maxf#28v r #29 i, 1 2 ; 0g S i , S i,1 r i , r i,1 , maxf,#28v r #29 i+ 1 2 ; 0g S i+1 , S i r i+1 , r i : #283#29 The boundary conditions given in Table1 involve only zero or #0Crst order derivatives. For the latter terms, #0Crst order back or forward di#0Berences can be used, except for two boundary conditions which require a more accurate treatment.... In PAGE 7: ... By comparing our numerical solutions with a primitivevariable solution of the same problem #5B19#5D, we found that these two boundary conditions exerted a strong in#0Duence on the overall accuracy of the numerical solution. The discretization of the partial di#0Berential equations #282#29 together with the boundary conditions #28 Table1 #29 yields a set of algebraic equations of the form F #28U#29 = 0, which is solved using a damped Newton method J#28U n #29#01U n = ,#15 n F #28U n #29; n =0;1;:::; #285#29 with convergence tolerance k#01U n k S #3C 10 ,5 . The Jacobian matrix J#28U n #29 is computed numerically using vector function evaluations and the grid nodes are split into nine independent groups which are perturbed simultaneously #28see #5B2#5D for more details#29.... ..."

### TABLE 1. Boundary Conditions

2008

### TABLE I BOUNDARY CONDITIONS

### Table1 Parameters in simulation of collapse of liquid column.

"... In PAGE 4: ... The simulation has been conducted at an aspect ratio of column n2= H/a=2 in a two-dimensional rectangular domain surrounded with non-slip solid walls. In both cases of spatial resolution ( Table1 ), initial column width a was assumed to be equivalent to 146mm in air- water system. Fig.... ..."

### Table 1 Boundary Condition Types

2004

"... In PAGE 39: ...Six types of boundary conditions are implemented in M2D, and these can be distinguished as specifying forcing and non-forcing boundaries. Table1 lists the boundary-condition types and contains a short description of each. Each boundary-condition type is described next.... ..."

### Table 1. Boundary Conditions for the f

"... In PAGE 8: ... Note that since the linear form of the pressure-strain rate model is used here, the value for C L di ers from that used previously (C L =0:2, see Manceau and Hanjali c 2000) for the form of the elliptic relaxation equation given in (11). Boundary conditions are needed for the f ij and are determined, in the vicinity of the wall, by the balance of the redistributivetermby the viscous di usion of the Reynolds stresses resulting in Table1 . Only the 22- and 12-components of f have determinate solutions to the near-wall balance of the stress transport equations.... In PAGE 19: ... n Boundary Conditions The expressions for the n boundary conditions are derived from the basis tensors T (n) ij used in the representation of f ij f ij = 3 X n=1 n ^ T (n) ij ! 8 gt; gt; gt; gt; gt; lt; gt; gt; gt; gt; gt; : f 11 = 2 T (2) 11 + 3 T (3) 11 f 22 = 2 T (2) 22 + 3 T (3) 22 f 33 = 3 T (3) 33 f 12 = 1 T (1) 12 (A1) Table1 gives the corresponding boundary conditions for these f ij components. The boundary condition for 1 is directly proportional to the f 12 boundary condition and is given by 1;;w = f 12;;w T (1) 12 = p 2f 12;;w = ;20 p 2 2 12 quot; 2 w y 4 (1) (A2) The coe cient 3 appears in all three expansions of the diagonal terms of f ij .... ..."

### Table 1: ATMI boundary conditions

2006

"... In PAGE 2: ... The conductance h2 between the copper layer and the ambient medium is computed as h2 = 1=(RhsL2), where Rhs is the heat sink thermal resistance and L is the heat sink width. Boundary conditions are listed in Table1 , where T1 and T2 are the temperatures in layers 1 and 2 respectively, and q(x;y; t) is the surface power density. The ff3d model is depicted on Figure 2.... ..."

Cited by 3