Among various numerical approaches for spatial discretization, the finite difference schemes are commonly used due to their computational efficiency and ease of implementation when higher order of accuracy is required. Most of the spatial differencing schemes are analyzed and optimized using one-dimensional test cases. As a result, in multidimensional problems they may not have isotropic behavior. This work is an extension of a previous one that proposed optimized two-dimensional finite difference schemes with improved isotropy for problems of Aeroacustics. The extension is to use the optimized onesided schemes to convection problems for stability improvement when steady state solution is sought. It is found that on a Cartesian grid not only the magnitude but also the direction of the local velocity is important in calculating the local time step. Compared to classical schemes, by using optimized schemes, the time step could be increased by 50% in some regions of the flow. Also, the artificial dissipation introduced by the upwind version of the optimized schemes is larger. These suggest the use of the optimized schemes as acceleration technique for steady problems. The centered and one-sided optimized schemes are validated by solving Aeroacustics problems and the Euler equations on Cartesian grids.
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