In the previous chapter, sample DNS results of incompressible chan-nel ows were presented, with discussions given on the numerical features of the methods used in the simulations. In contrast to incompressible ows, which are of relatively low speeds, compressible ows represent a broad range of uid ows with relatively high speeds, ranging from low compressible subsonic ows with Mach numbers slightly higher than 0.3, to highly compressible hypersonic ows with Mach numbers exceeding 5. Compressible ows have many applications, especially in aerospace engineering. DNS provides a very powerful tool to investigate compressible ows and to gain insight into the fundamentals of the ow, turbulence, and mixing processes at high speeds. An enhanced understanding obtained by DNS can help many practical applications in dierent ways, including the development of eective ow control techniques for aeronautics and astronautics. DNS results can be eectively utilized to interpret available experimental data, to guide experimental work, and to execute calculations for operating conditions that are not achievable using experimental methods. In many applications of compressible ows, DNS can provide results that are not possible or are dicult to obtain using experimental and/or analytical methods and other computational methods.