Model and simulation of dam-break problem

Abstract

The dam-break analysis is one of the problems that has greatly attracted the interest of researchers in the field of applied mathematics and fluid mechanics. One of the main issues is the suitability of numerical treatment to capture the sudden movement of water after the breaking of the dam. Hyperbolic systems of partial differential equations can be used to model a wide variety of phenomena that involve wave motion or advective transport of substances. For dam-break problem, such a system of equation is generally nonlinear which makes the problem too difficult to solve exactly. Numerical approximations are generally sought. Many numerical methods are now at hand to solve the model equations. Among these the finite volume formulation has been widely accepted in modeling strategy for its accuracy and robustness. Here, we shall improve its efficiency by including the adaptive mesh refinement method in the calculation of dam-break solution.