This report describes the development of a two-dimensional multi-material Eulerian hydrocode to model the effects of detonating condensed phase explosives on surrounding materials. The code solves the Euler equations for the conservation of mass, momentum, and energy for an inviscid, compressible fluid. Operator splitting is used to reduce the two-dimensional calculation into coupled one-dimens...

We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [1] and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number...

Compressed Sensing (CS) is a novel sampling paradigm that tries to take data-compression concepts down to the sampling layer of a sensory system. It states that discrete compressible signals are recoverable from sub-sampled data, when the data vector is acquired by a special linear transform of the original discrete signal vector. Distributed sampling problems especially in Wireless Sensor Netw...

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without...

Operator splitting is a numerical method of computing the solution to a differential equation. The splitting method separates the original equation into two parts over a time step, separately computes the solution to each part, and then combines the two separate solutions to form a solution to the original equation. A canonical example is splitting of diffusion terms and convection terms in a c...

To prevent epidemics of mosquito-transmitted diseases like Chikungunya in Réunion Island, we develop tools to control its principal vector, Aedes albopictus. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to environment. The success of SIT is based on a good knowledge of the biology ...

We show that the motion of a slightly compressible fluid is near that of an incompressible fluid. That is, for a given initial velocity field, the motion of a compressible fluid with large sound speed is near to that of an idealized incompressible fluid. We consider the compressible fluid motion in Lagrangian coordinates and show that it can be defined by two functions giving the kinetic and po...

We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary diierential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary diierential equation is solved exactly or by an explicit Euler method. We prove that ...

In this paper we treat subjects which are relevant in the context of iterative methods in implicit time integration for compressible flow simulations. We present a novel renumbering technique, some strategies for choosing the time step in the implicit time integration, and a novel implementation of a matrix-free evaluation for matrix-vector products. For the linearized compressible Euler equati...