A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations

Sultan Qaboos University Journal for Science

Mohammed Al-Lawatia¹  Robert C. Sharpley²  Hong Wang² 

[1] Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36 Al-Khod 123, Sultanate of Oman.;Industrial Mathematics Institute, Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA.;

关键词: Characteristics methods, Comparison of numerical methods, Eulerian-Lagrangian methods, Numerical solutions of advection-diffusion equations, Runge-Kutta methods.;   

DOI  :  10.24200/squjs.vol6iss2pp67-83

来源: DOAJ

【 摘 要 】

We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). The derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used.  Numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method.

【 授权许可】

Unknown