3D implicit mesh-less method for compressible flow calculations

An implicit mesh-less method is developed for calculation of compressible flows around three dimensional complex geometries. The algorithm is applied directly to the differential form of the governing equations using least-square formulation. A dual-time implicit time discretization scheme is developed, and the computational efficiency is enhanced by adopting accelerating techniques, such as local time stepping, residual smoothing and enthalpy damping. Two different artificial dissipation techniques are employed for stability preservation and it is shown that the scalar one is more efficient in terms of accuracy and computational time. The capabilities of the method are demonstrated by flow computations around different geometries under subsonic and transonic flow conditions. Results are presented which indicate good agreement with experimental and other reliable numerical data. The method is shown to reduce computational time by about 50% compared with the alternative explicit method.