In this work we present the study of a robust Finite Volume (FV) numerical scheme for solving the compressible Euler equations in 2D on highly anisotropic meshes for supersonic fluid flow applications. The first-order accurate FV scheme is first derived in a classical fashion focusing on the numerical flux and its property of maintaining the solution within the physical admissible set (positive density and specific internal energy) via a well-designed CFL condition. Next we present a second-order extension based on Strong Stability Preserving Runge-Kutta time discretization and piecewise linear spacial reconstruction of primitive variables limited thanks to entropy constraints. Again the limiting procedure coupled with a well designed CFL condition ensures that the numerical solution remains in the physical admissible set. This second-order FV scheme is further adapted to highly anisotropic meshes for which some extra dissipation procedure may be required to ensure robustness without sacrificing accuracy. In the case of steady state solution for supersonic fluid flows, an automatic iterative procedure is used to allow successive mesh adaptation in a sequential order, coupled with solution projection from one mesh to the next adapted one. We will present academic test cases as well as validation tests to assess the robustness and accuracy of the whole simulation framework. One typical test case is the simulation of the hypersonic Mach 20 fluid flow around a cylinder.