2 Discussion of the Riemann problem

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2 Discussion of the Riemann problem

In the following we will concentrate on the time evolution of our flow model from an initial state that consists of two semi-infinite uniform zones which are separated by a discontinuity. One can imagine a realization of this situation by positioning a diaphragm ("infinitely thin dam") between the two fluid states and somehow rupture it at time t=0. Our objective is to determine the resulting induced wave motion as a function of the initial state. This problem is geometrically one-dimensional in that the solution only depends on one space coordinate normal to the diaphragm, say x*e_n. In this section we will first restrict our analysis to one-dimensional motion, i.e. v=u*e_n, and the flat-bottom case without bottom friction, viz.

We will return to the two-dimensional case and the question of a non-uniform bottom at a later point.

• 2.1 Characterization of the system of equations
• 2.2 Analytic solution to Riemann's problem

2 Discussion of the Riemann problem

Contents

Index