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The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…
We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the…
The classic Stoker dam-break problem is revisited in cases of different channel widths upstream and downstream of the dam. The channel is supposed to have a rectangular cross section and a horizontal and frictionless bottom. The system of…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…
In this paper, we present an extension of the Generic Second Order Models (GSOM) for traffic flow on road networks. We define a Riemann solver at the junction based on a priority rule and provide an iterative algorithm to construct…
We introduce in this contribution the notion of partial Riemann problem. Recall that the Riemann problem describes a shock tube interaction between two given states ; the partial Riemann problem is a generalization of the previous concept…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…
We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…
A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. It has been demonstrated that the addition of a viscous…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…
We examine the classical joint source--channel coding problem from the viewpoint of statistical physics and demonstrate that in the random coding regime, the posterior probability distribution of the source given the channel output is…
A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general,…
This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In…
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the…