SUMMARYA dual-time implicit mesh-less scheme is presented for calculation of compressible inviscid flow equations. The Taylor series least-square method is used for approximation of spatial derivatives at each node which leads to a central difference discretization. Several convergence acceleration techniques such as local time stepping, enthalpy damping and residual smoothing are adopted in this approach. The capabilities of the method are demonstrated by flow computations around single and multi-element airfoils at subsonic, transonic and supersonic flow conditions. Results are presented which indicate good agreements with other reliable finite-volume results. The computational time is considerably reduced when using the proposed mesh-less method compared with the explicit mesh-less and finite-volume schemes using the same point distributions.

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a b s t r a c tUsing the artificial compressibility (AC) approach for incompressible flows, the NavierStokes equations are coupled together to obtain solutions for steady flows, where marching in time methods are applicable. In this study, we present a new method that employs the multidimensional characteristics of AC equations to calculate the solid boundary conditions. The first multidimensional characteristic-based scheme (MCB) for incompressible flows was proposed in a previous study. In the present study, this idea is implemented by using the characteristic structure of AC equations near solid walls together with a ghost cell method to satisfy the solid boundary conditions. We test the new proposed method with two well-known benchmark problems, where the results show that the accuracy and convergence speed of the MCB scheme is improved in many cases.