In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this formulation the junctions disappear since each path is considered as a single uninterrupted road. We consider a Godunov-based approximation scheme for the system which is very easy to implement.

We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in the Heston model, showing the reliability and the efficiency of the algorithm.

The study of a planing flat plate may be considered as a topic of wide interest for academic and industrial applications. From experimental and numerical studies, flow separation occurs near the stagnation point and a thin jet sprays forward along the plate, while a clear wave pattern develops downstream. In the present study, the effect on the jet-root position caused by a cushion pressure applied on the downstream free surface is considered and the consequent variation in lift and drag coefficients is studied.

The analysis of a propeller operating in off-design conditions is one of the most attractive and challenging topics in naval hydrodynamics, because of its close connections with different aspects of ship design and performances. For these reasons, wake dynamics and propeller loads are analyzed in the present paper by means of a numerical code based on the solution of the Reynolds averaged Navier-Stokes equations, whose capability to capture propeller hydrodynamics in these extreme conditions are also investigated.

A Boundary Element Method (BEM) hydrodynamics combined with a flow-alignment technique to evaluate blades shed vorticity is presented and applied to a marine propeller in open water. Potentialities and drawbacks of this approach in capturing propeller performance, slipstream velocities, blade pressure distribution and pressure disturbance in the flow-field are highlighted by comparisons with available experiments and RANSE results. In particular, correlations between the shape of the convected vortex- sheet and the accuracy of BEM results are discussed throughout the paper.

The onset and the nature of dynamic instabilities experienced by the wake of a marine propeller set in oblique flow are investigated by means of detached eddy simulations. In particular, the destabilization process is inspected by a systematic comparison of the wake morphology of a propeller operating in pure axisymmetric flow and in drift with angle of 20 degrees, under different loading conditions.

The flowfield inside the second solid stage of the European launch vehicle VEGA is simulated with a full 3D unsteady flow solver in order to characterize the unsteadinesses, aero-acoustics and dynamics loads resulting from the growth of complex vorticity patterns in the internal flow of the aft-finocyl solid rocket motor.

We prove global existence and uniqueness of smooth solutions to a nonlinear system of parabolic-elliptic equations, which describes the chemical aggression of a permeable material, like calcium carbonate rocks, in presence of acid atmosphere. This model applies when convective flows are not negligible, due to the high permeability of the material. The global (in time) result is proven by using a weak continuation principle for the local solutions.

Indefinite symmetric matrices occur in many applications, such as optimization, least squares problems, partial differential equations, and variational problems. In these applications one is often interested in computing a factorization of the indefinite matrix that puts into evidence the inertia of the matrix or possibly provides an estimate of its eigenvalues. In this paper we propose an algorithm that provides this information for any symmetric indefinite matrix by transforming it to a block antitriangular form using orthogonal similarity transformations.