This paper discusses the convergence of a new discrete-velocity model to the Boltz-mann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modiied model to DiPerna-Lions solutions of the Boltz-mann equation. As a test numerical example, the solutions to the discrete problems are compared to the exact solut...

This paper introduces a nonlinear reduced-order modelling methodology for finite-element models of structures with slender subcomponents and inertia represented by lumped masses along main load paths. The constructed models have dynamics described by 1-D intrinsic equations of motion, which are further written in modal co-ordinates. This yields finite-dimensional approximations of the system dy...

Avalanches of various sizes occur due to instability during sand dune dynamics. A physically viable equation to model sand dune dynamics is a first order nonlinear difference equation. To visualize the size distribution of avalanches, sand dune dynamics has been numerically simulated by changing the strength of nonlinearity parameter (λ) that shows different impacts on dune dynamics. An equatio...

Abstract The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on simplex system of equations gas dynamics in the mixed Euler-Lagrangian variables. To find solution such scheme at time step, it represented as single equation nonlinear function two arguments from space – direct product spaces gas-dynamic quantities. ...

Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation-now called the Boltzmann equation-for the phase space density of the molecules of a dilute fluid. He showed that the Second law of thermodynamics emerges from Newton's equations of motion. Ho...

Identi cation results for the shaft-speed dynamics of an aircraft gas turbine, under normal operation, are presented. As it has been found that the dynamics vary with the operating point, nonlinear models are employed. Two di7erent approaches are considered: NARX models, and neural network models, namely multilayer perceptrons, radial basis function networks and B-spline networks. A special att...

introduction: the main objective of the present study was to investigate the effect of preceding pictorial stimulus on the emotional autonomic responses of the subsequent one. methods: to this effect, physiological signals, including electrocardiogram (ecg), pulse rate (pr), and galvanic skin response (gsr) were collected. as these signals have random and chaotic nature, nonlinear dynamics of t...

A three-dimensional computational fluid dynamics model of a proton exchange membrane fuel cell (PEMFC) with both gas distribution flow channels and Membrane Electrode Assembly (MEA) is developed. A set of conservation equation is numerically solved by developing a CFD code based on the finite volume technique and SIMPLE algorithm. In this research, some parameters like oxygen consumption, water...

In this work, the novel iterative transformation technique and homotopy perturbation are used to calculate fractional-order gas dynamics equation. technique, iteration method combined with Elzaki transformation. The current methods implemented four examples show efficacy validation of techniques. approximate solutions obtained by given techniques that accurate easy apply other linear nonlinear ...