schemes for solving this equation are well known. Generally speaking, numer- 

 ical accuracy can be improved somewhat by taking a smaller time step for a 

 given space step, assuming negligible numerical truncation error. Increased 

 computer execution time is the price paid for using smaller time steps. 

 Therefore, one wants to balance speed of the calculation with numerical 

 accuracy. 



75. Numerical accuracy should be distinguished from "physical" accu- 

 racy. Numerical accuracy is a measure of how well a finite difference scheme 

 reproduces the solution of a differential equation; physical accuracy is a 

 measure of how well the differential equation (and the numerical solution if 

 one is employed) describes the process of interest. 



76. For an explicit scheme, there is a stringent limitation (the 

 Courant condition) on the size of the largest possible time step, other vari- 

 ables being held constant. For small breaking wave angles, in the present 

 case this condition is 



R < \ (31a) 



s - d. 



where 



2 K 1 At (H 2 C 



R = ^T^ (31b) 



s d uxr 



The quantity R was called the "stability parameter" by Kraus and Harikai 

 (1983). Equation 31a is an adequate indicator of stability in most applica- 

 tions, since breaking wave angles are usually small. The stability parameter 

 gives an estimate of the numerical accuracy of the solution, with accuracy 

 typically increasing for decreasing values of R g . 



Example 1 : Jetty and Detached Breakwater 



77. The initial condition is shown in Figure 9a. The initially 

 straight 2,000-m stretch of beach is protected by a shore-parallel, detached 

 breakwater and a seawall connected to a long jetty. The seawall is set back 

 7 m from the initial shoreline. The jetty is assumed to be sufficiently long 

 so as to act as a complete littoral barrier. The breakwater is drawn in Fig- 

 ure 9 to aid visual understanding; in actuality, it lies much farther off- 

 shore. The seawall and breakwater have been constructed to prevent erosion 



32 



