Abstract: A method for the adaptive refinement of a Quad/Cartesian grid for the solutions of the Euler and N-S equations is presented.An adaptive Quad/Cartesian hybrid grid method,which retains the advantages of the Cartesian grid approach and, at the same time, touches the viscous flow problems,is provided.The body fitted Quad grids are generated around the body and the Cartesian grids are used in the remains of the flow field.The flow solver of the Euler and N-S equations is performed by a conventional algorithm,including the finite volume method and the Runge-Kutta time-stepping scheme.The grid adaptation and the flow solver achieve reasonable efficiency and accuracy with minimum computer resources.Based on the above approach,the numerical analysis of flows around the single-element and the multi element airfoils is given.The numerical results presented show the flexibility of this approach and the accuracy attainable by the solution-based refinement.

Key words: adaptive refinement, Quad/Cartesian hybrid grid, N-S equations