Advective Effects in the Numerical Simulation of Long Period, Large Amplitude Wave Behavior

Numerical modeling of water-wave behavior has progressed rapidly in the last decade and is now generally recognized as a useful tool capable of providing solutions to many coastal problems. The U. S. Army, through various agencies, has sponsored development of two-dimensional numerical models for simulating long period wave behavior. Many of these models have included the advective terms in their formulation. Demonstrated in numerous papers throughout the literature, inclusion of advective effects can lead to instabilities in the solution. This fact was exemplified in the work of Sloss (1972) in his attempt to include these effects in storm surge simulation. The primary objective of this investigation was the assessment of the role of advective terms in the numerical simulation of long period, large amplitude wave behavior. A major effort in accomplishing this objective was the development of an appropriate representation of the non-linear terms in the difference equations of motion. To this end, a stabilizing correction, double sweep implicit scheme was encoded into an existing and extensively used hydrodynamic model, WIFM. The scheme manifested a high degree of stability in various numerical flume tests.