1. The Governing Equations The hydrodynamic model adopted here is the one based on the hydrostatic pressure approximation and the boussinesq approximation, and fixed layer divisions in vertical discretization. A set of governing equations is required to compute four unknowns, which are three velocity components and the water level. Introduction Change of flow pattern due to human intervention cause water quality degradation. The change can create stagnation regions that have limitation on oxygen supply. Representation of physical condition, i.e. the flow pattern, is necessary before any ecological model can be used. In many three-dimensional flow calculation, wetting-drying process hasn’t been included in the calculation. Calculation of flow with wetting-drying scheme is necessary as part of conservation plan at tidally influenced area, coastal wetland for example. Coastal wetland forms a unique environment that supports nearby waters. The numerical hydrodynamic model with wetting drying scheme will be suitably applied to hydraulic studies in Segara-Anakan because of its shallow bathymetric condition due to sedimentation. The Numerical Model This model basically follows the procedure introduced by Sato et al. (1993) with addition of baroclinic term to take into account the effect of density gradient. Similar procedure is also found in Casulli and Cheng (1992). The difference between the two comes from different approaches that are used for solution of water level coupled tridiagonal linear system resulted from semi-implicit dicretization. Steps of research Purwanto Bekti Santoso (1), Nastain (2), Wahyu Widiyanto (3) Literature cited Casulli, V., and Cheng, R. T., 1992. Semi-Implicit Finite Difference Methods for Three-Dimensional Shallow Water Flow, Int. Jour. for Numerical Methods in Fluids, 15, 629-648. Sato, K., Matsuoka, M., and Kazumitsu, K., 1993. Efficient calculation method of 3-D tidal current. Proceedings of Coastal Engineering, JSCE, Vol.40, 221- 225.(in Japanese) DEVELOPMENT OF A HYDRODYNAMIC NUMERICAL MODEL WITH WETTING-DRYING CAPABILITY (1) Department of Civil Engineering, Universitas Jenderal Soedirman, Purwokerto, Indonesia, e-mail: purwanto250@yahoo.compurwanto250@yahoo.com (2) Department of Civil Engineering, Universitas Jenderal Soedirman, Purwokerto, Indonesia, e-mail: tain93@yahoo.comtain93@yahoo.com (3) Department of Civil Engineering, Universitas Jenderal Soedirman, Purwokerto, Indonesia, e-mail: wahyu_wdy75@yahoo.comwahyu_wdy75@yahoo.com Fig. 1. Land-ocean interface of hydrodynamics model a) with and b) without wetting-drying process List of symbols (u,v,w): flow velocity in direction of (x,y,z)  : free surface elevation g: gravitation f: coriolis parameter  0 : constant reference density  ’(x,y,z,t): local variation to reference density h and v : horizontal and vertical eddy viscosity H: still water level depth h: water depth C: concentrations of transported substances/temperature LSX: vertical index of top layer LEX: vertical index of bottom layer Treatment of the wetting-drying process Targets 1.A hydrodynamics numerical model with wetting-drying capability 2.Recommendation on friction coefficient and grid size high tide low tide mwl moving boundary a) with wetting-drying process high tide low tide mwl fix boundary minimum depth b) without wetting-drying process Horizontal Momentum Equations (calculation of horizontal flow velocity) Continuity equation (calculation of vertical flow velocity) Depth averaged continuity equation with kinematics boundary conditions ( calculation of water level) u i,j u i+1,j v i,j v i,j+1  i,j+1  i-1,j  i,j, C i,j  i+1,j  i,j-1 a) Horizontal Grid u LSX,i+1,j w LSX,i,j w LSX+1,i,j u LSX,i,j u LSX+1,i+1,j k=LSX k=LSX +1 u LEX- 1,i+1,j w LEX-1,i,j w LEX,i,j u LEX-1,i,j u LEX,i+1,j u LEX,i,j k=LEX -1 k=LEX u LSX+1,i,j SHX k,i,j = depth of flux faces at i-direction C LSX,i,j C LSX+1,i,j C LEX+1,i,j C LEX,i,j b) Vertical Grid Fig. 2. Variables arrangement of a) horizontal grid b) vertical grid Finite difference form of x momentum equation is arranged to the following form: Coefficients of {F1X k, F2X k, GX k } are obtained form calculation. Finite difference form of y momentum equation is arranged to the following form: Coefficients of {F1Y k, F2Y k, GY k } are obtained from calculation. (1) and (2) are substituted into the depth averaged continuity equation resulting in system of linear equations with unknown variable of  n+1, which is solved by using SOR (Successive Over Relaxation) method. Using water level  n+1 calculated from (3), equations (1) and (2) calculate u k n+1 and v k n+1 respectively. Then, vertical velocity w k n+1 is calculated from the mass conservation equation. time step update 1 2 3 4 Fig. 3. Step of calculation x-direction : Water level Bottom Fig. 4. Definition of water level in wetting-drying formulation If H zero, dry condition If H positive, wet condition If H zero friction factor is assumed to be infinite, then the momentum equations become: u i+1,j n+1 = 0 v i,j+1 n+1 = 0 Step 1. Implementation of the wetting-drying scheme on three- dimensional hydrodynamic model. Coding of Casulli dan Cheng (1992) wetting drying scheme into Fortran 77 code considering the structure of available three dimensional hydrodynamic code. Step 2. Testing the resulted code by comparison with analytical results Grid spacing 250 m, Time step 10 s, Tidal period 12 hours, Simulation time 4 tidal period, Friction factor 0.001 5 m 0.25 m 20 km a) Linear case 1 6 m 1.0 m 18 km b) Linear case 2 Step 3. Testing of hypothetical case. 1.Impact on stability due to implementation of wetting drying scheme 2.Sensitivity of friction factor to wetting-drying process 3.Sensitivity of grid size to wetting-drying process There are two cases. 1.Linear cases (1 and 2) 2.Quadratic case Grid spacing 250 m, time step 10 s, tidal period 12 hours, simulation time 4 tidal period, friction coefficient 0.001 Bathymetric map, Tidal data, Water level, Current, Wind, River discharge (Citanduy and Cibeureum) Step 4. Description of Segara Anakan Lokasi Studi Verification and calibration will be carried by using data of: 1.Water level (2 locations) 2.Current (2 locations) Step 5. Application of model to real condition (Segara Anakan). Simulation will be conducted to calibrate and verify the model by comparison with field data of Segara Anakan Fig. 5. Linear cases to be compared with analytical solution Fig. 6. Quadratic cases Fig. 7. Segara anakan