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Unformatted text preview: MPO 662 – Problem Set 5 The pupose of this homework is to write a onedimensional shallow water solver using secondorder schemes that can be viewed as either finite difference methods or finite volume methods, the discrete equations being the same. An important consideration is the need to conserve mass and view the continuity equation from a flux conservation point of view a la finite volume. The homework should then evolve the advection code you already have to a finite volume one, and activate an evolution equation for the velocity (which is nolonger a constant in space and time, but function of both). An added consideration is the need to deal with staggered grids. In writing your code you should reuse as much as possible from the codes you have already written, whether it is the ODE solver or the grid partitioner, or the advection code. The linearized shallow water equations are given by u t + gη x = 0 (1) η t + U x = 0 (2) where U = ( H + αη ) u is the depth integrated transport in the xdirection. Notice that when H = g = 0 and α = 1, the continuity equation becomes a simple advection equation, whereas...
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 Spring '08
 Iskandarani,M
 Numerical Analysis, finite difference, Finite difference method, Finite differences, finite volume

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