Impact of the Peclet Number on Numerical Solutions of Modified Convection-Diffusion Equations Using Berger's Equation

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.

Peclet number, numerical solution, modified Convection-Diffusion Equation, Burger’s Equation, Finite Difference Schemes, and Stability Conditions

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