PERI KUALITATIF PERSAMAAN DIFFERENSIAL TERPILAH UNTUK GELOMBANG KEJUT SUNAMI

Abstract

Gadunov provides insight to the general solution of Riemann problem by considering the
shock as a  local phenomena,and treated accordingly as  local problem. Two dimensional
exact analytical Riemann problems may be very difficult to solve. Another approach is to
split the two dimensional wave problem into 1D Riemann problem, where the analytical
solution is already known. To apply 1D Riemann problem into  two dimensional wave
problems, one has to discretize to the flow domain, into discrete non-overlapping elements,
control volume  or  cells. If the elements are the control volumes, then we can employ the
finite volume discretization scheme. Based on the schemes the hydrodynamic problems can
be solved elegantly by transforming the domain into non-overlapping control volume
elements and treated each elements as the local Riemann problem. This can be carried out
by transforming the global physical coordinates into local one, foe every discrete flow
elements (the control volume or cell), where the direction of flow axis is aligned with the
fluxdirection. The problem is then solved as hydrodynamic fluxes,  F, crossing the cells
interfaces. The  disadvantage  of this scheme is that the  control volume  —representing
gravitation and friction—is elimated from the equation, and therefore it seems to be not
realistic. However, integration of the characteristics with the source included, it can be
concluded that the source influence can be ade as small as possible by applying the proper
aselection of the time step (Abbot, 1979). In this case, we are treating the problem as solving
the Riemann quasi-invariants. The  influence of neglecting the source term will be reflected
in the amount of flux. If this influence is positive, the flux will be less than if the source term
is negative, i.e the source term is sink which decreases the momentum content, otherwise it is
a source which increases which increases the momentum flux. The influence must be
persistence, e.g in dissipative flow regime, neglecting the source term Riemann equation will
result in persistencelarger momentum flux compare to the real flow. This error may be less
or greater than numerical error. (see Numerical test # 1). Therefore, when applied to the
discretisized river sistem, the persistence rules will not be always reproduced in the
simulation result. This alternating positive and negative effect will be reflected by plotting
the numerical test value against the laboratory of field value or by complete numerical value
without neglecting the gravitational and friction effects (see simulation test of Osher scheme
in Kissimmee river , Florida, USA).
Keywords : local problem, control volume, control volume, control volume, shock wave