An Unconditionally Stable Numerical Scheme for 3D Coupled Burgers’ Equations

In this study, we sought numerical solutions for three-dimensional coupled Burgers’ equations. Burgers’ equations are fundamental partial differential equations in fluid mechanics. They integrate the characteristics of both the first-order wave equation and the heat conduction equation, serving as crucial tools for modeling the interaction between convection and diffusion. First, the fractional step method was applied to decompose the equations into one-dimensional forms. Then, implicit finite difference approximations were used to solve the resulting one-dimensional equations. To assess the accuracy of the proposed approach, we tested it on two benchmark problems and compared the results with existing methods in the literature. Additionally, the symmetry of the solution graphs was analyzed to gain deeper insight into the results. Stability analysis using the von Neumann method confirmed that the proposed approach is unconditionally stable. The results obtained in this study strongly support the effectiveness and reliability of the proposed method in solving three-dimensional coupled Burgers’ equations.