Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem

On the relevance of the dam break problem in the context of nonlinear shallow water equations

The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration...

Invesstigation of Dam Break Problem through solution of 1D-Shallow water equations using Fourth order Runge-Kutta Method, McCormack’s Method and Gudonov’s Method

On the Physical Relevance of the Dam Break Problem in the Context of Nonlinear Shallow Water Equations

The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

Efficient scheme for the shallow water equations on unstructured grids with application to the Continental Shelf

In this paper, a shallow-water flow solver is presented, based on the finite-volume method on unstructured grids The method is suitable for flows that occur in rivers, channels, sewer systems (1D), shallow seas, rivers, overland flow (2D), and estuaries, lakes and shelf breaks (3D). We present an outline of the numerical approach and show three 2D test cases and an application of tidal propagat...