Simulations of transonic inviscid flows over airfoils using meshfree adaptive algorithm

A new mesh free algorithm, which is both solution and geometry adaptive, is introduced and described in this paper to capture the physical features of inviscid flows modeled by the Enter equations. Only clouds of points instead of grids are distributed over the computational domain and he spatial derivatives of the Enter equations are estimated using a weighted least-square curve fit on local clouds of points. The adaptive approach is compared to traditional global refinement techniques using structured grids. In this procedure, unnecessary '' grid '' points in adjacent area are prevented from being generated by using mesh free local clouds refinement techniques. These techniques operate. in particular, in the vicinity of shock influencing regions and near large curvature regions including the boundary surface of the geometry. Several numerical experiments with Euler flow simulation around airfoils at transonic regimes will be presented to illustrate the potential of this methodology in terms of accuracy, efficiency and low computer memory requirement of the mesh free adaptive algorithm.