Upwind Schemes For The Linear Convection Equation
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Date
2007-06
Authors
Zunaira Zaka
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Abstract
Many important physical processes in nature are governed by partial differential
equations. Analytical methods of solving partial differential equations are usually
restricted to linear cases with simple geometries and boundary conditions. The
increasing availability of more and more powerful digital computers has made more
common the use of numerical methods for solving such equations.
There are many different approaches to solving partial differential equations
numerically, but in this dissertation only finite difference methods are studied. The
basic theory of finite difference schemes applied to numerical solution of partial
differential equations and fundamental concepts of convergence, consistency and
stability are reviewed. In particular for solving the one dimensional linear convection
equation, explicit techniques based on the weighted finite difference approximations
.tare presented. Convectional explicit finite difference schemes for solving the one
dimensional linear convection equation are subjected to time step restrictions dictated
by the CFL condition.
The aim of this dissertation is to compare several explicit upwind difference
schemes for solving the one dimensional linear convection equation which are
considered both theoretically and by means of illustrative numerical examples.
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Keywords
To compare several explicit upwind difference schemes for solving , the one dimensional linear convection equation