Numerical Solution of Burgers Equation Using Finite Difference Methods: Analysis of Shock Waves in Aircraft Dynamics

In this research, the Lax, the Upwind, and the MacCormack finite difference methods are applied to the experimental solving of the one-dimensional (1D) unsteady Burger's Equation, a Hyperbolic Partial Differential Equation. These three numerical analysis-solving methods are implemented for accurate modeling of shock wave behavior high-speed flows that are necessary for aerospace engineering design. This research analysis proves that the MacCormack technique is the one that treats the differential equations with second-order accuracy. This method is quite preferred when it comes to numerical simulations because of its advanced level of accuracy. Although the Upwind and Lax methods are slightly less accurate, they show the development of shock waves that give visualizations to better understand the flow dynamics. Also, in this study, the impact of varying viscosity coefficients on fluid flow characteristics by using the lax (a numerical method for solving the viscous Burgers equation) is investigated. This identification of the phenomenon sheds light on the behavior of boundary layers, which, in turn, can be used to improve the design of high-speed vehicles and lead to a greater understanding of the area of ​​fluid dynamics.