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.