limiting value on the size of the time step in relation to the space step. 

 The method of characteristics employing a characteristic network was applied 

 to flood flows by Amein (1966) and Fletcher and Hamilton (1967). Baltzer and 

 Lai (1968) applied the fixed-mesh method of characteristics to tidal flows in 

 estuaries. The impetus for the development of an implicit method was the need 

 for accurate and flexible solution methods that could allow use of large time 

 steps, thereby shortening the computation time. 



37. Implicit schemes for writing difference equations to represent the 

 partial differential equations and methods for the solution of the resulting 

 difference equations have been introduced by various authors. Thomas (1934) 

 was probably the first to propose an implicit four-point grid. Implicit grid 

 schemes have been proposed by Cunge and Wegner (1964) , Preissmann (1971) , 

 Isaacson (1966), Lai (1967), Liggett and Woolhiser (1967), Abbott and lonescu 

 (1967), and others. A double-sweep method is described by Strelkoff (1970). 

 Most of the earlier methods introduced some form of linearization to the 

 finite-difference equations and devised schemes to avoid simultaneous solution 

 of algebraic equations. Isaacson (1966) used a finite -difference scheme 

 centered both in time and space in the study of the dam-break problem. The 

 nonlinear algebraic equations were solved by Newton iteration. 



38. Amein (1968) presented an implicit solution method employing 

 centered finite-differences for the numerical simulation of flood flows. The 

 nonlinear algebraic equations were solved by generalization of the Newton 

 iteration method. Although the procedure requires solution of a large system 

 of simultaneous equations, by taking advantage of the sparseness and handed- 

 ness of the coefficient matrix, a rapidly convergent and very accurate 

 solution method was developed. The method was extended to natural and irregu- 

 lar channels by Amein and Fang (1970) , to power plant transients and reser- 

 voirs by Amein and Chu (1975) , and to a tidal inlet network by Amein (1975) . 



39. The two main technical objectives of the present study are to 



further extend the implicit solution method of Amein (1972, 1975) to realize a 



practical numerical model for analyzing tidal inlet flows and to demonstrate 



the validity of the model. Newly added features of the model developed in 



this study include: 



a. Allowing variable bottom elevations and friction coefficients 

 at user-specified locations across channel cross sections. 



16 



