Abstract
This paper deals with numerical modelling of supersonic flow of cone and sphere bodies using the penalty function method. The main objective of the study is to evaluate the effectiveness of the penalty function method, also known as the immersed boundary method, for solving compressible gas dynamics problems. We apply modified Navier-Stokes equations considering streamlined bodies and use the ENO scheme for the numerical solution. The simulation results demonstrate that the proposed approach successfully describes the physical processes occurring in the supersonic flow of a cone and sphere, including the formation of shock waves, pressure, temperature and density distributions. The obtained data are compared with experimental results, confirming the adequacy and accuracy of the developed numerical model. The presented work contributes to the development of methods for numerical modelling of compressible supersonic flows and demonstrates the promising use of the penalty function method for solving a wide class of gas dynamics problems.