The variable n accounts for hydrostatic water elevations due to atmospheric 



pressure differences, and F and F represent external forces such as wind 

 f ' X y ^ 



stress. 

 Numerical method 



14. The alternating-direction-implicit (ADI) method has been used by 

 Leendertse (1970) and others to solve the two-dimensional equations of motion. 

 When the advective terms are included in the momentum equations (Equa- 

 tions 8, 9) the ADI method has encountered stability problems. Weare (1976) 

 indicates that the problems arise from approximating advective terms with 

 one-sided differences in time and suggests the use of a centered scheme with 

 three time-levels. WIFM employs a centered stabilizing-correction (SC) scheme 

 which is second-order accurate in space and time, and boundary conditions can 

 be formulated to the same order of accuracy. A brief development of the SC 

 scheme is presented in the following paragraphs. Note that x] and h are 

 defined at the cell center and u and v at the cell faces. 



15. The linearized equations of motion can be written in matrix form 

 as: 



U + AU + BU =0 

 t X y 



(10) 



where 



U = 



A = 



'o d o" 

 goo 

 o o o. 



B = 



'o o d" 

 o o o 

 g o o. 



The SC scheme for solving Equation 10 is 



17 



