A finite difference solution of the Euler equations on non-body-fitted Cartesian grids☆

Abstract A finite difference solution on non-body-fitted Cartesian grids has been developed for the two-dimensional compressible Euler equations. The solution is based on the method of lines. The spatial derivatives of the Euler equations are first discretized by finite difference approximations on stretched grids. The rational Runge-Kutta scheme is used as the time-stepping scheme. Accurate numerical boundary conditions are introduced at the body surfaces where the coordinate lines do not generally fit the boundaries. A series of numerical experiments are carried out to validate the present solution. Numerical results obtained for transonic flows over single-element airfoils agree well with reliable results obtained for the same flows on body-fitted grids. Typical numerical results are also obtained for transonic flows over bi-NACA0012 airfoils. The present solution is confirmed to be easily tractable even for multielement flow fields.

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