Page - 482 - in Book of Full Papers - Symposium Hydro Engineering

                uuuuuu u u u u t u 321                    2222                 uuuu hJ uCHH g xx n yy f yyxxyx                    (2) h Fuu rtrt                                        22                 uuuuuu u u u u t u 654                    2222                  uuuu hJ uCHH g xxyy f yyxxyx                    (3) h Fuu rtrt                                        22 In these equations,  and  = the spatial coordinate components in the boundary fitted curvilinear coordinate system; t = the time coordinate in the coordinate system; J = Jacobian of the coordinate transformation given as yxtyxtyxtJ               xytyxtyxt             ;  u and  u = contravariant components of the depth-averaged flow velocity in the  and  directions, respectively, defined as vuu yx      and vuu yx      ; u and v = the depth averaged velocity components in x and y directions, respectively. The coefficients 1 ~ 6 are given in Jang and Shimizu (2005). The morphodynamic module of Nays2DH includes sediment transport, bank erosion, and bed elevation changes. The two-dimensional sediment continuity equation in boundary-fitted coordinate system is as follows: 0 1 1                                            J q J q J z t bbb (4) where bz = bed elevation;  = porosity of the bed material;  bq and  bq = contravariant components of the bedload transport rate per unit width in the  and  directions, respectively. The sediment transport rate in the stream line is calculated using the formula of Ashida and Michiue (1972). As a numerical scheme, the cubic interpolated psuedoparticle (CIP) method is used. The numerical method solves boundary problems while introducing little numerical diffusion, and algorithm implementation is more straightforward than for other high-order upwind. In the non-advection phase, the continuity equation and the non-advection terms in the momentum equations are solved for depth as a Poisson equation. The viscous terms are approximated using the central difference method. Readers are referred to Jang and Shimizu (2005) for more details. 3. APPLICABLITY OF NUMERICAL MODEL 482