D-4 Wave Forecast System of Hualien Harbour by Jaw-Guei Lin ...

2008 Taiwan-Polish Joint Seminar on Coastal Protection∂φ∂nΩ2Ω2−αφΩ2= 0on solid boundary Γ3(4)where α = ik [( 1−K R) ( 1+K R)], KRis the reflection coefficient, and nΩ 1and nΩare2the unit normal vectors directed outware from the domain Ω1and Ω 2respectively.On pseudo boundary Γ4, the scatter waves φSshould satisfy the Sommerfeld radiationcondition⎛ ∂ ik ⎞lim r ⎜ ⎟−φS= 0r→∞⎝ ∂rλ ⎠By applying the first variation theory, the functional F ( φ)of the entire area can beconstructed.122 2F( φ ) = ∫∫( λCCg∇φΩ− CCgkφΩ) dA112+12∫∫Ω 2Ω122 2( λCC∇ φ − CC k φ )dAgSgS(5)−−12∫ΓΓαλCCφ dL +112 1∫αλCCgφSdL −2232g Ω1∫ΓλCC2∫Γ4g∂φ0φΩ∂nΩCCg2ik φSdLλ22dL(6)After introducing the finite/infinite elements into the discretization of equ (6). Thestationary of the functional F ( φ)implies that∂F= 0 , i = 1,2,... N(7)∂φiwhere N is the number of nodal point. The velocity potential at each node of entirearea can then be solved.Fig3. Definition sketch of the harbour tranquility modelD-40