The shape of a nozzle wall influences the phenomena associated with the behaviour of the fluid movement within the flow field mathematically described by the Navier—Stokes equations. This article studies different drawing techniques for the aerodynamic tracing of the wall contour searched by Vitoshinsky, Bell, Metha and Sivells. To the system of equations of the design models are added the math formulas that define Sauer’s method for redesigning the length of the converging section modifying simultaneously the contour sketches. The aim is to obtain a better distribution of the physical properties and to avoid excessive pressure in a limited space that could affect the internal structure of the wall. Numerical methods are used to visualize the features of the wave propagation, boundary layer separation and flow separation pattern to survey the appearance of the stream generated within the geometric profile of the wall and the ejected flow. A computational analysis is developed to make a comprehensive assessment of different chosen wall contours, including an optimized wall shape using genetic algorithms through a process to find maximum and minimum values of the cross-sectional area to change the wall layout. The selection carries out based on design parameters with variable area contraction ratio (from low to high) in the convergent section for being simulated in a boundary condition with a low-pressure ratio (NPR). Experimental data from Hunter's research are used for validation of the results for a J2-type aerospace nozzle operating at an NPR of 3.413.