A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

2008 ◽  
Vol 111 (2) ◽  
pp. 169-205 ◽  
Author(s):  
Alina Chertock ◽  
Alexander Kurganov
Keyword(s):  
Second Order ◽  
Upwind Scheme ◽  
Positivity Preserving

A positivity-preserving nonlinear finite volume scheme for radionuclide transport calculations in geological radioactive waste repository

2019 ◽  
Vol 30 (2) ◽  
pp. 516-534 ◽  
Author(s):  
Gang Peng ◽  
Zhiming Gao ◽  
Wenjing Yan ◽  
Xinlong Feng
Keyword(s):  
Radioactive Waste ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Radionuclide Transport ◽  
Positivity Preserving ◽  
Content Type ◽  
Radioactive Waste Repository ◽  
Convection Diffusion ◽  
Waste Repository ◽  
Second Order Convergence

Purpose This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository. Design/methodology/approach The nonlinear two-point flux approximation is used to discretize the diffusion flux and has a fixed stencil. The cell-vertex unknowns are applied to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. The approximation of convection flux is based on the second-order upwind method with a slope limiter. Findings Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes. Originality/value A new positivity-preserving nonlinear finite volume scheme is proposed to simulate the far-field model used in the geological radioactive waste repository. Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

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.

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
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