In this work the numerical simulations of a submarine in straight ahead motion with the appendages at several prescribed deflection angles are performed. Due to the complex geometry involved (the presence of moving appendages), these simulations are rather demanding form the point of view of both grid generation and accuracy of the numerical method. In order to analyze these aspects, the numerical solutions are computed by means of an unsteady Reynolds averaged Navier-Stokes equations solver, which is particularly effective because of the high order discretization schemes adopted.

The authors study the convergence and the stability of a collocation and a discrete collocation method for Cauchy singular integral equations with weakly singular perturbation kernels in some weighted uniform norms. Uniform error estimates are also given. © 1997 Rocky Mountain Mathematics Consortium.

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This class coincides for a=0 with the Symm's euqtion. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists in substituting this in the experrsion of the solution g.

In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make it possible to tune the degree of predictiveness of the individuals.

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This equation can be transformed into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists of applying the Lagrange interpolation to the inner Cauchy type singular integral in the latter formula after subtracting the singularity. For the error of this method weighted norm estimates as well as estimates on discrete subsets of knots are given.

The results of accurate compressible Navier-Stokes simulations of aerodynamic heating of the Vega launcher are presented. Three selected steady conditions of the Vega mission profile are considered: the first corresponding to the altitude of 18 km, the second to 25 km and the last to 33 km. The numerical code is based on the mathematical model described by the Favre-Average-Navier-Stokes equations; the turbulent model chosen for closure is the one-equation model by Spalart-Allmaras.