A stable second-order mass-weighted upwind scheme for unstructured meshes

2006 ◽  
Vol 51 (7) ◽  
pp. 749-771 ◽  
Author(s):  
Luu Dung Tran ◽  
Christian Masson ◽  
Arezki Smaïli
Keyword(s):  
Unstructured Meshes ◽  
Second Order ◽  
Upwind Scheme

Evaluation and Comparison of Bounding Techniques for Convection-Diffusion Problems

1993 ◽  
Vol 115 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. A. R. Sharif ◽  
A. A. Busnaina
Keyword(s):  
Velocity Field ◽  
Second Order ◽  
Upwind Scheme ◽  
Numerical Dispersion ◽  
Test Problems ◽  
Analytical Treatment ◽  
Numerical Diffusion ◽  
Convection Diffusion ◽  
Uniform Velocity ◽  
Flux Corrected Transport

The effects of bounding the skew upwind and the second-order upwind discretization schemes for the convection terms in convection-diffusion transport equations have been studied. Earlier studies indicated that these two schemes produce less numerical diffusion but introduce unacceptable numerical dispersion or oscillations in the solution if not bounded. A simplified analytical treatment exploring the reason for this behavior is presented. Two bounding techniques, the flux-corrected transport and the filtering remedy and methodology were evaluated. Test problems used in the evaluation are (i) one-dimensional convection of a rectangular pulse, (ii) transport of a scalar step in a uniform velocity field at an angle to the grid lines, (iii) Smith and Hutton problem, (iv) two-dimensional convection of a square scalar pulse in a uniform velocity field at an angle to the grid lines, and (v) two interacting parallel streams moving at an angle to the grid lines. The results indicate that the flux-corrected transport eliminates the oscillations in the solution without introducing any additional numerical diffusion when used with both schemes. The filtering remedy and methodology also eliminates the oscillation when used with the skew upwind scheme. This technique, however, is not effective in reducing the over-shoots when used with the second-order upwind scheme.

scholarly journals High-resolution central-upwind scheme for second-order macroscopic traffic flow models

2020 ◽  
Vol 31 (07) ◽  
pp. 2050097
Author(s):  
Jianzhong Chen ◽  
Ronghui Liu ◽  
Yanmei Hu
Keyword(s):  
High Resolution ◽  
Traffic Flow ◽  
Approximation Method ◽  
Numerical Approximation ◽  
Second Order ◽  
Upwind Scheme ◽  
Flow Models ◽  
Macroscopic Traffic Flow ◽  
Traffic Flow Models ◽  
Macroscopic Traffic Flow Models

Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models.

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

2018 ◽  
Vol 358 ◽  
pp. 103-129 ◽  
Author(s):  
Walter Boscheri ◽  
Michael Dumbser ◽  
Raphaël Loubère ◽  
Pierre-Henri Maire
Keyword(s):  
Finite Volume ◽  
Unstructured Meshes ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Volume Scheme

Transient Analysis of Multi-Conductor Transmission Line Based on the Second-Order Upwind Scheme

2014 ◽  
Vol 543-547 ◽  
pp. 821-824
Author(s):  
Yin Han Gao ◽  
Jun Dong Zhang ◽  
Kai Yu Yang ◽  
Tian Hao Wang ◽  
Yu Zhu ◽  
...  
Keyword(s):  
Transmission Line ◽  
Time Domain ◽  
Splitting Method ◽  
General Purpose ◽  
Second Order ◽  
Upwind Scheme ◽  
Application Process ◽  
Discontinuous Solutions ◽  
Leapfrog Scheme ◽  
Line Coupling

On the basis of the second-order upwind scheme, combined with the flux splitting method, we derive a uniform multi-conductor transmission line time-domain calculations. This method is a direct time-domain discrete numerical method with second order accuracy. It does not have any special requirements for circuit and the application process and complex transformations which lead to facilitate the preparation of the program. Numerical experiments show that this method of preparation of general purpose computing program has roughly the same computational efficiency with the traditional leapfrog scheme and at the discontinuous solutions, there are no non-physical oscillations. It can easily be used to calculate a uniform multi-conductor transmission line coupling.

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