Marco Tessarotto

The Lagrangian dynamics of thermal tracer particles in Navier-Stokes fluids

A basic issue for Navier-Stokes (NS) fluids is their characterization in terms of the so-called NS phase-space classical dynamical system, which provides a mathematical model for the description of the dynamics of infinitesimal (or ideal) tracer particles in these fluids. The goal of this paper is to analyze the properties of a particular subset of solutions of the NS dynamical system, denoted as thermal tracer particles (TTPs), whose states are determined uniquely by the NS fluid fields. Applications concerning both deterministic and stochastic NS fluids are pointed out. In particular, in both cases it is shown that in terms of the ensemble of TTPs a statistical description of NS fluids can be formulated. In the case of stochastic fluids this feature permits to uniquely establish the corresponding Langevin and Fokker-Planck dynamics. Finally, the relationship with the customary statistical treatment of hydrodynamic turbulence (HT) is analyzed and a solution to the closure problem for the statistical description of HT is proposed.

Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e., continua) is usually related to the so-called ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution.

Lagrangian Dynamics of Incompressible Thermofluids

A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental importance, the issue is relevant to exhibit the connection between fluid dynamics and the classical dynamical systems underlying incompressible and non-isothermal fluid, typically founded either on: a) a \textit{configuration-space} Lagrangian description of the dynamics of fluid elements; b) a kinetic description of the molecular dynamics, based on a discrete representation of the fluid. The goal of this paper is to show that the exact Lagrangian dynamics can be established based on the inverse kinetic theory (IKT) for incompressible fluids recently pointed out (Ellero \textit{et al.}, 2004-2006, \cite{Ellero2004}). The result is reached by adopting an IKT approach based on a \textit{restricted phase-space representation} of the fluid, in which the configuration space coincides with the physical fluid domain. The result appears of potential importance in applied fluid dynamics and CFD.

Modelling of Anthropogenic Pollutant Diffusion in the Atmosphere and Applications to Civil Protection Monitoring

A key aspect of fluid mechanics concerns the frictionless phase‐space dynamics of particles in an incompressible fluid. The issue, besides its theoretical interest in turbulence theory, is important in many applications, such as the pollutant dynamics in the atmosphere, a problem relevant for civil protection monitoring of air quality. Actually, both the numerical simulation of the ABL (atmospheric boundary layer) portion of the atmosphere and that of pollutant dynamics may generally require the correct definition of the Lagrangian dynamics which characterizes arbitrary fluid elements of incompressible thermofluids. We claim that particularly important for applications would be to consider these trajectories as phase‐space trajectories. This involves, however, the unfolding of a fundamental theoretical problem up to now substantially unsolved: namely the determination of the exact frictionless dynamics of tracer particles in an incompressible fluid, treated either as a deterministic or a turbulent (i.e., ...

XML-VM: An XML-Based Grid Computing Middleware

This paper describes a novel distributing computing middleware named XML-VM. Its architecture is inspired by the ‘Grid Computing’ paradigm. The proposed system improves many characteristics of previous Grid systems, in particular the description of the distributed computation, the distribution of the code and the execution times. XML is a markup language commonly used to interchange arbitrary data over the Internet. The idea behind this work is to use XML to describe algorithms; XML documents are distributed by means of XML-RPC, interpreted and executed using virtual machines. XML-VM is an assembly-like language, coded in XML. Parsing of XML-VM programs is performed with a fast SAX parser for JAVA. XML-VM interpreter is coded in JAVA. Several algorithms are written in XML-VM and executed in a distributed environment. Representative experimental results are reported.

The Computational Complexity of Traditional Lattice‐Boltzmann Methods for Incompressible Fluids

It is well‐known that customary direct solution methods (based on the discretization of the fluid fields) for the fluid equations of incompressible fluids may be affected by a high computational complexity. This is due primarily to the numerical solution of the Poisson equation for the fluid pressure and occurs when the scale‐length of turbulent fluctuations becomes comparable to the discretization scale which characterizes the numerical solution method. An alternative, which can reduce significantly the complexity caused by the numerical solution of the fluid equations for incompressible fluids, may be achieved by so‐called particle simulation methods. In such a case the dynamics of fluids is approximated in terms of a set of test particles which advance in time in terms of suitable evolution equations defined in such a way to satisfy identically the Poisson equation. Particle simulation methods rely typically on appropriate kinetic models for the fluid equations which permit the evaluation of the fluid ...