scholarly journals A Comparative Numerical Study on Freeway Weaving Area using a Multi-class First-order Macroscopic Model

2016 ◽  
Author(s):  
Saeed Mohammadian ◽  
Abolfazl Mohammadzadeh Moghaddam ◽  
Ali Sahaf
Keyword(s):  
Numerical Study ◽  
Macroscopic Model ◽  
First Order

Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subal Ranjan Sahu ◽  
Jugal Mohapatra
Keyword(s):  
Time Delay ◽  
Numerical Study ◽  
Singularly Perturbed ◽  
Parabolic Differential Equations ◽  
Small Space ◽  
First Order ◽  
Taylor Series Approximation ◽  
Backward Euler ◽  
Differential Difference Equation ◽  
Negative Space

Abstract A time dependent singularly perturbed differential-difference equation is considered. The problem involves time delay and general small space shift terms. Taylor series approximation is used to expand the space shift term. A robust numerical scheme based on the backward Euler scheme for the time and classical upwind scheme for space is proposed. The convergence analysis is carried out. It is observed that the proposed scheme converges almost first order up to a logarithm term and optimal first order in space on the Shishkin and Bakhvalov–Shishkin mesh, respectively. Numerical results confirm the efficiency of the proposed scheme, which are in agreement with the theoretical bounds.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

Numerical Study of Superharmonic Resonances in a Mistuned Horizontal-Axis Wind-Turbine Blade-Rotor Set

2019 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Wind Turbine ◽  
Initial Conditions ◽  
Numerical Study ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
First Order ◽  
Direct Excitation ◽  
Rotor Angle ◽  
Perturbation Solutions

Abstract This paper is on a simplified model of an in-plane blade-hub dynamics of a horizontal-axis wind turbine with a mistuned blade. The model has cyclic parametric and direct excitation due to gravity and aerodynamics. This work follows up a previous perturbation study applied to the blade equations written in the rotor-angle domain and decoupled from the hub, in which superharmonic and primary resonances were analyzed. In this work, the effects of mistuning, damping, and forcing level are illustrated. The first-order perturbation solutions are verified with comparisons to numerical simulations at superharmonic resonance of order two. Additionally, the effect of rotor loading on the rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.

Macroscopic Model and Its Numerical Solution for Two-Flow Mixed Traffic with Different Speeds and Lengths

2003 ◽  
Vol 1852 (1) ◽  
pp. 209-219 ◽  
Author(s):  
Stéphane Chanut ◽  
Christine Buisson
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Macroscopic Model ◽  
Model Output ◽  
Mixed Traffic ◽  
Traffic Flow Model ◽  
Hyperbolic Conservation ◽  
Flux Function ◽  
First Order ◽  
Proposed Model

A new first-order traffic flow model is introduced that takes into account the fact that various types of vehicles use the roads simultaneously, particularly cars and trucks. The main improvement this model has to offer is that vehicles are differentiated not only by their lengths but also by their speeds in a free-flow regime. Indeed, trucks on European roads are characterized by a lower speed than that of cars. A system of hyperbolic conservation equations is defined. In this system the flux function giving the flow of heavy and light vehicles depends on total and partial densities. This problem is partly solved in the Riemann case in order to establish a Godunov discretization. Some model output is shown stressing that speed differences between the two types of vehicles and congestion propagation are sufficiently reproduced. The limits of the proposed model are highlighted, and potential avenues of research in this domain are suggested.

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