Explicit and Implicit Finite -Volume Methods for Depth Averaged Free-Surface Flows

Abstract

In recent years, much progress has been made in solving free-surface flow variation problems in order to prevent flood environmental problems in natural rivers. Computational results and convergence acceleration of two different (explicit and implicit numerical techniques) finite-volume based numerical algorithms, for depth-averaged subcritical and/or supercritical, free-surface, steady flows in channels, are presented. The implicit computational model is a bi-diagonal, finite-volume numerical scheme, based on MacCormack’s predictor-corrector technique and uses the semi-linearization matrices for the governing Navier-Stokes equations which are expressed in terms of diagonalization. This implicit numerical scheme puts primary emphasis to solution convergence using non-orthogonal local coordinate system. The explicit formulation uses volume integrals to solve the governing flow equations. Computational results and convergence performance between the implicit and the explicit finite-volume numerical schemes, for incompressible, viscous, depth-averaged free-surface, steady flows are presented. Implicit and explicit computational results are satisfactorily compared with available measurements. The implicit bi-diagonal technique yields fast convergence compared to the explicit one at the expense of programming effort. Iterations require to achieve convergence solution error of less than 10-5, can be reduced down to 90.0 % in comparison to analogous flows with using explicit numerical technique.

Keywords

• explicit integral method
• implicit bidiagonal finite-volume
• water depth