Penurunan Persamaan St. Venant Untuk Dasar Berbagai Kasus Dinamika Fluida

Abstract

The shallow water wave’s equation represents rapid unsteady flow frequently attended by shock waves. For shock phenomena, the influence of bottom friction may be assumed marginal, as the bottom width where shock arises is relatively very thin compared to the scale of the flow domain. However, the energy loss across the shock is significant. This energy loss is attributed to the internal stresses within the very thin infinitesimal shock interface. For practical computation, the contribution of the internal friction may be incorporated in the wall friction, in other words the internal stresses can be represented as Manning frictional resistance. Frictions either wall friction, surface friction, or internal friction between fluid particles are the sources or sinks of momentum. Strong simplification of modeling of the free surface shallow flows is necessary for the computer simulation. The material on the basis of shallow water models is essential, even considering a numerical method of any kind, similar to most of the shock-capturing numerical methods on the utilisation of local Riemann problem solution, both for the exact or approximate. However the role of the Riemann problem is wider. The Riemann problem can be useful in theoretical studies of simple shalow water models; it can also be used in conjunction with other numerical solution. This research deals with shock-capturing, finite volume numerical methods, particular devoted to the details of numerical methods of the shock-capturing type. Some hypothetical tests are modeled as a shallow water wave equation, which therefore can be cast as Riemann Problem, solved by utilizing the Godunov’s type solution. Finite volume methods of the Godunov type are used for the purpose of solving numerically the time-dependent, non-linear shallow water equations. Key words : shallow water, homogeneous, shock, sources, sinks, Riemann problem, finite volume, shock-capturing, Godunov’s type.