When a shock wave interacts with a contact discontinuity, there may appear a reflected rarefaction wave, a deflected contact discontinuity and a refracted supersonic shock. The numerical simulation of shock wave refraction at a plane contact discontinuity separating gases with different densities is performed. Euler equations describing inviscid compressible flow were discretized using the finite volume method on unstructured meshes and WENO schemes. Time integration was performed using a third-order Runge-Kutta method. The wave structure resulting from regular shock refraction is determined allowing its properties to be explored. In order to visualize and interpret the results of numerical calculations, a procedure for identifying and classifying gas-dynamic discontinuities was applied. The procedure employed dynamic consistency conditions and digital image processing methods to determine flow structure and its quantitative characteristics. The results of the numerical and experimental visualizations were compared (shadow patterns, schlieren images, interferograms). The results computed are in an agreement with the theoretical and experimental predictions of a regular refraction of a shock wave on an inclined contact discontinuity.