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Identifier

uch.math.msc//2005stefa

Title

Αριθμητικές Μέθοδοι για τις εξισώσεις των Ρηχών Υδάτων

Alternative Title

Numerical Methods for the Shallow Water Equations

Author

Στέφα, Βασιλική

Abstract

In the present work we discuss a special class of conservation laws, the one-dimensional Shallow Water Equations, with a geometrical source term (the bottom topography). Namely, Ut + F(U)x = S(U); where, U = · h hu Έ; F(U) = · hu hu2 + g 2h2 Έ; S(U) = · 0 ‘ghZ0 Έ: This system describes the flow at time t Έ 0 at point x 2 R where h(x; t) Έ 0 is the total water height above the bottom, u(x; t) is the average horizontal velocity, Z(x) is the bottom height function and g the gravitational acceleration. The most important property of this system is that they preserve steady states and satisfying an entropy condition. To discretize the above system we proceed as follows. First we introduce the relaxation approximation of JinXin for the shallow water equation. We proceed by discretizing the relaxation system using finite differences schemes of first and second order and implicitexplicit RungeKutta methods as time stepping mechamisms. Key words: shallow water equations; relaxation schemes; finite differences

Language

Greek

Issue date

2005-03-17

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Views

388

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