User's Manual and Examples for GNWAVE

Abstract

Source: https://erdc-library.erdc.dren.mil/jspui/This report describes the operation and use of a new numerical model, GNWave. This model was designed to simulate the evolution of a train of two-dimensional waves in waters of arbitrary bottom topography, varying from shallow water to waters of moderate depth. The program uses the Green-Naghdi theory of fluid sheets as its model, and integrates a set of coupled, nonlinear partial differential equations in time to perform the simulation of surface gravity waves. Report 1 in this series, entitled "Application of the Green-Naghdi theory of fluid sheets to shallow water wave problems," contains a detailed description of the mathematical basis of GNWave model. The model GNWave has been shown to reproduce with engineering accuracy the evolution of a wave of permanent form, from small amplitudes up to almost breaking conditions. The numerical model is portable with little or no changes to a wide variety of platforms, and has successfully been tested on high-end PC's and VAX and CRAY mainframe systems. The governing equations were programmed using Fortran as the language. The program consists of a main program and a number of modules to perform the calculations. A functional flow chart of individual routines involved in the computation is included herein. The main routine directs the sequence of the calculation, including the reading of the input and integration of the equations, and performs some post-processing. The main program is divided into two basic segments: an input portion where the specifications of the problem are read in and echoed to the computer screen, and an integration portion where the equations are integrated one time step at a time. Output is produced at pre-specified instants in the computation stages. The calculation involves four basic components: generation of waves at the ocean end of the wave tank, enforcement of an appropriate boundary condition at the shore end of the computational domain, solution of the two-point boundary value problem in space at a given instant in time, and integration of the equations in time. Each of these four components requires special techniques, which are discussed in this report to give the user an overview of the flow of information and a flavor for the computation that occurs during a simulation. To further assist the reader in understanding the implementation of the code, the algorithms used for wave generation, the treatment of beach-end boundary conditions, and the spatial and temporal integration of the governing equations are explained in the body of this report. Model input and output features are also presented, together with the procedure for using the program and the restart mode of operation of the model. Five example problems typically encountered in the military and civil works areas of the US Army Corps of Engineers are presented. These include collision of waves with a hydraulic spillway gate, waves transforming over an open-ended sloping beach, pseudo-spectral waves passing over a sand bar, random waves propagating through a dredged navigation channel, and regular waves shoaling on a landing beach of uniform slope. The first example problem tests the model's capability for a reflective boundary while the second problem checks the implementation of the transmissive or open type boundary condition. Simulation results for problems 3 and 4 are compared to illustrate the effects of a sand bar on the down-wave progressing in a channel. The last problem provides an opportunity to check the model simulation against physical model test data from a laboratory study conducted at the Danish Hydraulic Institute. The model has been shown to reproduce with engineering accuracy the evolution of regular and irregular wave trains up to the almost breaking condition