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Numercial Simulation for Two Dimension Water Contamination Problem
Author: JiangLi
Tutor: XieShuSen
School: Ocean University of China
Course: Computational Mathematics
Keywords: Convection-diffusion equation Fractional step method p - r Law WENO scheme Error Analysis
CLC: O242.1
Type: Master's thesis
Year: 2010
Downloads: 98
Quote: 0
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Abstract
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Three - dimensional convection-diffusion problem is reduced to two-dimensional problem easier to handle , equivalent to only consider the convection-diffusion motion of the plane direction , regardless of the vertical material deposition . Fractional step method for the two - dimensional convection-diffusion problem into a two - dimensional convection problem and two-dimensional diffusion problem . PR method is a toggled direction algorithm, in dealing with the two-dimensional diffusion problem unconditionally stable nature , its accuracy is only second-order , and can not be extended to three dimensions . Convection-diffusion equation meaningful Convection diffusion equation, processing Convection diffusion equation is to solve the numerical simulation of the convective term . General upwind scheme and the Lax - Wendroff format low accuracy in the calculation of the convection equation , calculation steps S.Osher and Chi - wang Shu WENO ( weighted essentially non- shock ) format using the Newton interpolation and stream function notation Europe the pull-up equation, the method having a high precision characterized in space , and can effectively capture shock . Taking into account the calculation of the diffusion term with second-order accuracy , precision the WENO three-point computational convection equation of the second order spatial discretization . Finally, Strang method is used to further reduce the fractional step method for error . In this paper, Runger - Kutta method WENO scheme applied to the solution of the diffusion equation, and a numerical example to illustrate this application is feasible .
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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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