In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resoluti...

Contents 1. Introduction 2. The two-dimensional models of overland flow 3. The equations of one-dimensional channel flow 4. Simplification of the St. Venant equations 5. Linearization of the St. Venant equations and solution of linear equations 6. Kinematic wave equations and their application 7. Numerical solution of the unsteady flow equations 8 Application of finite elements methods 9. Lumpe...

This paper proposes a new time-scaling approach for computational optimal control of a distributed parameter system governed by the Saint-Venant PDEs. We propose the time-scaling approach, which can change a uniform time partition to a nonuniform one. We also derive the gradient formulas by using the variational method. Then the method of lines (MOL) is applied to compute the Saint-Venant PDEs ...

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating ...