An adaptive method for the solution of compressible flows is described. The idea results from the desire for an efficient grid system,and an accurate and robust solution method are used to resolve flow features of the interest. The adaptation flow solution is proposed,including the detection of flow features based on the matrix error; the mesh adaptation using the mesh movement,the mesh refinement,the mesh coarsening,and their combination. The feature detection based on the matrix error can maintain the high resolution property for shock waves of the one-dimensional approximate Riemann solver and the higher order reconstruction scheme. The high grid efficiency is obtained with the anisotropically directional grid corresponding to feature directions,and the error of the flow-field is averaged. The procedure and its application to flow solutions of shock waves are described. Results validate that the method is reliable.
