CMS-Flow:Implicit

Under Construction

Introduction

Time marching schemes can be classified into two major groups, explicit and implicit. Explicit schemes obtain the solution for the next time step based solely on solution(s) of previous time step(s). Implicit schemes on the other hand, obtain the solution of the next time step based on the solution of previous and current time steps. Although the explicit model is simple and efficient, its time step is limited in the case of shallow water equations by the computational grid. In order to increase computational speed. The implicit solver has been implemented for the hydrodynamic, sediment and salinity calculations.

Numerical Methods

The hydrodynamic, sediment transport and salinity equations are solved using the Finite Volumen Method on a non-uniform rectangular quad-tree (telescoping) grid. The governing equations are descretized using a non-staggered (collocated) grid in which all variables are calculated at the cell center. The collocated grid is convenient because it reduces data storage and simplifies the computation. The hydrodynamic equations equations are solved using the Semi-Implicit Method for Pressure-Linked Equations Consistence of van Doormaal and Raithby (1984). Inter-cell fluxes are computed with the Momentum Interpolation method of Rhie and Chow (1983). The water depths are specified at the cell centers and are linearly interpolated to cell faces. A first order fully implicit time marching scheme is implemented.