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A dual-time implicit mesh-less method is presented for unsteady compressible flow calculations. Polynomial least-square (PLS) and Taylor series least-square (TLS) procedures are used to estimate the spatial derivatives at each node and their computational efficiencies are compared. Also, the effect of the neighbor stencil selection on the accuracy of the method is investigated. As a new approach, different neighboring stencils are used for the highly stretched point distribution inside the boundary layer region and the inviscid isotropic point distribution outside this area. The unsteady flows over stationary and moving objects at subsonic and transonic flow conditions are solved. Results indicate the computational efficiency of the method in comparison with the alternative approaches. The convergence histories of the flow solution show that the PLS method is computationally faster than TLS method. In addition, the eight point neighboring stencil inside the viscous region is more efficient than other choices.

Three di erent adaptive methods are presented for meshless calculation of steady and unsteady ows. Two approaches of point re nement/coarsening and point movement have their ground in the mesh-based methods that, in the present work, are extended for meshless calculations. However, the third approach is a new concept, socalled adaptive neighboring scheme, that concerns the optimum selection of the neighbors for each point in the meshless framework. This means that the selection of the neighboring region for each particular point is a ected by the ow features in the domain. In this paper, an explicit meshless method based on the least square scheme is used. The results are presented for di erent steady and unsteady ows and the e ciency of the methods in terms of computational cost and accuracy is investigated. It is observed that using these adaptive approaches decrease the computational cost of the method by about 60% as compared with the un-adapted results while improving the accuracy of results at the same time.

The main aim of this paper is to develop an e cient aeroelastic tool for predicting the utter speed of a typical section in transonic regime. An implicit meshless method, based on Euler and Navier-Stokes equations, is conducted to simulate the transonic uid ow around an airfoil. This technique is applied directly to the di erential form of the aerodynamic governing equations and the time integration is carried out using a dual-time implicit time discretization scheme. The capabilities of the ow solution method are demonstrated by ow computations around NACA0012 airfoil under di erent ow conditions. For structural dynamics simulation, a typical section model with pitching and plunging motion capability is considered. Finally, the aeroelastic analysis of the 2D model is performed by the consecutive simulation of both structural and aerodynamic domains. Also, the e ect of viscosity and time interval choice between two structural and aerodynamic solvers on utter instability is studied. A comparison between the obtained results and those available in the literature shows the good accuracy of the present method.