A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume.This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms.The presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element.The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations.Furthermore,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be passive.The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is known.The new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.

Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scaling.This means that,in the limit of zero mean free path,the system is governed by a drift-diffusion equation.Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations:the kinetic,the intermediate and the diffusive one.Moreover,we want to overcome the restrictive time step conditions of standard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy.As a result,we obtain high order time and space discretization schemes which do not suffer from the usual parabolic stiffness in the diffusive limit.We show different numerical results which permit to appreciate the performances of the proposed schemes.