Impact of the Peclet Number on Numerical Solutions of Modified Convection-Diffusion Equations Using Berger's Equation
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The study investigates the influence of the Peclet number on the numerical solutions of modified convection-diffusion equations, specifically utilizing Berger's equation as the governing model. Finite difference methods has been employed to solve Convection diffusion equation under different Peclet numbers, analyzing the resulting numerical behavior, including solution profiles, error propagation, and computational efficiency. The findings reveal that as the Peclet number increases, the dominance of convective terms introduces numerical instabilities, such as oscillations and excessive diffusion, necessitating the implementation of specialized discretization techniques or stabilization methods. The study also explores the effectiveness of upwind schemes and adaptive mesh refinement in mitigating these challenges.
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References
Roache, P. J. (1972). Computational Fluid Dynamics. Hermosa Publishers.
Fletcher, C. A. J. (1991). Computational Techniques for Fluid Dynamics. Springer-Verlag.
Berger, M. J. (1984). "Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations." Journal of Computational Physics, 53, 484-512.
Changjun Zhu and Shuwen Li, “Numerical Simulation of River Water Pollution Using Grey Differential Model,” Journal of computers, Vol. No.9, 2010.
D.J. Evans, A.R. Abdullah, The group explicit method for the solution of Burger’s equation, Computing 32 (1984) :239-253.
A. Kumar, D. K. Jaiswal and N. Kumar, Analytical solution of one-dimensional Advection diffusion equation with variable coefficients in a finite domain, J. Earth Syst. Sci. 118, No.5, pp. 539-549, October 2009.
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