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Unformatted text preview: MPO 662 – Problem Set 5 The pupose of this homework is to write a one-dimensional shallow water solver using second-order 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 no-longer 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 re-use 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 x-direction. Notice that when H = g = 0 and α = 1, the continuity equation becomes a simple advection equation, whereas...
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- Spring '08
- Numerical Analysis, finite difference, Finite difference method, Finite differences, finite volume