    The objective of this research is to study the formation of a separation bubble over a 2D half-body by Reynolds Averaged Navier-Stokes (RANS) simulation. This numerical simulation technique uses a reduced computational data and has been adopted for most practical engineering problems, since the design of such applications relies on the steady state flow and average velocity field. The main purpose is to analyze the flow dynamics of the recirculation bubble for dimensionless parameter η = R/H (ratio of rounded radius and body height). One case is investigated, corresponding to η = 0.25. The Reynolds number, based on the free-stream velocity U∞ and the height of the obstacle H, is equal to Re = 2000. The solutions obtained through the Reynolds Averaged Navier-Stokes (RANS) equations for the two-dimensional steady state flow uses the Spalart-Allmaras and SST (Shear Stress Transport) κ-ω models. These RANS models assume isotropic modeling of the Reynolds tensor. The results are compared with computational data.

The dynamic study of colliding objects is an important branch of study in engineering due to recurrence of impacts in real situations such as car crashes, gunshot or bird impacts, for example. The pressure profiles are determined by shock wave propagation phenomena, where the stress tensor determination is necessary for the development of new materials and structures, regarding aspects such as safety. Numerical simulation can be applied to approximate the solution of shock wave problems where materials are submitted to high strain rates. In this paper a methodology to simulate problems involving shock wave propagation is present. To avoid numerical complications associated with highly distorted grid due the large deformation, the numerical meshless method smoothed particle hydrodynamic (SPH) was employed to approximate the derivative governing equations. As the methodology is general this work aims academic objectives, and to be applicable the only changes are in the initial conditions of particles. To evaluate the numerical code a particular case with analytical solution was tested, a one-dimensional plate impact ignoring the deviatory stress showed a percentage error less than 0.1665 % in pressure profiles. Another two-dimensional impact example was presented in this work with the deviatory tensor considered.impact a target plate with a circular hole. The results are compared with the case of a target plate without the hole. The constitutive model adopted was the elastic perfectly plastic and the deviatory was considered. METHODOLOGYThis section provides the mathematical development of shock wave propagation in a condensate medium.