/•-'-•-'—•—_» . 



x» ^ ^ 



Nearshore Circulation Pattern, constant viscosity 

 Physical Model Pattern shown dotted 



Figure 36. Nearshore circulation pattern, constant 

 viscosity; physical model pattern shown 

 dotted (from Bettess, et al. , 1978). 



accuracy for propagation-type problems. The locally one-dimensional implicit 

 method (Mitchell and Griff iths, 1980)'*° was employed to efficiently and numeri- 

 cally integrate the equations. The weighting coefficient between upper and 

 lower time levels 6 of the two level scheme is adjustable for efficient steady- 

 state solutions (0 = 1) or accuracy (6 = i^) i^ unsteady flows. All the 

 space derivatives are centered. 



Considerable discussion is presented by Vreugdenhil (1980) regarding 

 stability, numerical accuracy, and the boundary conditions. Complete details 

 are beyond the scope of this report but such analyses are critical to the 

 quantitative success of any ntjmerical simulation. For example, the direction- 

 al nature and repetition of the solution procedure for the x-direction and 

 y-direction sweeps (using either locally one-dimensional or alternating direc-. 

 tion implicit methods) will affect the amount of numerical viscosity or dif- 

 fusion generated. Numerical viscosity can easily be much greater than the 

 eddy viscosity even for schemes using centered space derivations for the con- 

 vective acceleration terms. For steady-state solutions, spatially oscillating 

 solutions (wiggles) in the velocity fields can be generated even in linearly 

 stable schemes. These come from the nonlinear convective acceleration terms 

 and can be artificially damped by using large eddy coefficients at the expense 

 of numerical accuracy. The relationships between boundary conditions, bed 

 friction, internal, lateral eddy viscosity, ntimerical viscosity (truncation 



40 



MITCHELL, A.R. and GRIFFITHS, D.R. , The Finite Difference Method in Partial 

 Differential Equations ^ Wiley-Inters cience, J. Wiley and Sons, New York, 

 1980 (not in bibliography). 



130 



