Numerical Study of the Characteristics of Shock and Rarefaction Waves for Nonlinear Wave Equation

In everyday life human faces shock waves and rarefaction largely in their surroundings. Hence it’s necessary to know the behavior of these protect destructive effects. The aim this work observe propagation various dynamics due solve non-linear hyperbolic inviscid Burgers’ equation numerically. models adopted here two numerical schemes which enable us first order explicit upwind scheme (EUDS) second Lax-Wendroff are used improve our understanding diffusion (smearing) oscillations that can be present when using such schemes. understand solution we use method characteristics find exact equation. Numerical solutions studied for different initial conditions investigated Riemann problem. We stability analysis establish condition leads determine time step selection terms spatial size with maximum value. result compared an accuracy by error estimation. features rate convergence presented graphically. This helps a wide range physical phenomenon properties wave as well saves several aspects real life.