PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, there is a lack of high-order schemes. We propose a Runge-Kutta discontinu- ous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of water flow in open canals. Our numerical tests show the advantages of RKDG over first-order schemes.

A {0, 1}-matrix A is balanced if it does not contain a submatrix of odd order having exactly two 1's per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrary to what happened for perfect graphs. In this paper, we provide such a characterization for the class of diamond-free graphs and establish a connection between minimally unbalanced diamond-free graphs and Dyck-paths.

We study a hybrid tree/finite-difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.

In this paper we consider the final distribution of fuel oil from a storage depot to a set of petrol stations faced by an oil company, which has to decide the weekly replenishment plan for each station, and determine petrol station visiting sequences (vehicle routes) for each day of the week, assuming a fleet of homogeneous vehicles (tankers). The aim is to minimize the total distance travelled by tankers during the week, while loading tankers possibly near to their capacity in order to maximize the resource utilization.

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps. In this talk, we consider the numerical approximation of such models. On one hand, due to the non-local nature of the integral term, we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions.

We present a lattice Boltzmann (LB) model for the simulation of hemodynamic flows in the presence of compliant walls. The new scheme is based on the use of a continuous bounce-back boundary condition, as combined with a dynamic constitutive relation between the flow pressure at the wall and the resulting wall deformation. The method is demonstrated for the case of two-dimensional (axisymmetric) pulsatile flows, showing clear evidence of elastic wave propagation of the wall perturbation in response to the fluid pressure.

A mathematical model describing the bioventing technique for the decontamination of pol- luted subsoil will be presented. Bioventing is a biological technique: bacteria remove the contaminant transforming it and oxygen is consumed in the reaction. The numerical model is based on the fluid flow theory in porous media and bacteria population dynamics and it describes: pollutant degradation, oxygen and bacteria concentration. The mathematical model will be numerically solved and the results of some experiments will be presented.

Well-balanced schemes were introduced to numerically enforce consistency with longtime behavior of the underlying continuous PDE. When applied to linear kinetic models, like the Goldstein-Taylor system, this construction generates discretizations which are inconsistent with the hydrodynamic stiff limit (despite it captures diffusive limits quite well).