Numerical modelling of compressible flows around moving solids is important for engineering applications such as aerodynamic flutter, rocket engines and landing gear. The penalty function method is particularly effective when using orthogonal structural meshes within a finite difference scheme and is widely used to solve both laminar and turbulent flow problems. The method is based on the direct application of the Navier-Stokes equations with added sources, which allows the boundary conditions to be set indirectly. This method facilitates the imposition of Dirichlet boundary conditions but complicates the application of Neumann conditions. Nevertheless, the method works well with both types of boundary conditions, making it suitable for thermal and compressible flows where Neumann conditions are often used. Despite its flexibility, the method requires a high degree of data management and additional coding. This paper presents results of a recently developed higher-order method for compressible subsonic flows, demonstrating accurate modeling of moving objects without numerical noise. The method has been tested on stationary and moving objects over a wide range of Reynolds and Mach numbers