scholarly journals Ray Theory for High-Péclet-Number Convection-Diffusion

1999 ◽  
Vol 60 (1) ◽  
pp. 121-135 ◽  
Author(s):  
S. J. Chapman ◽  
J. M. H. Lawry ◽  
J. R. Ockendon
Keyword(s):  
Peclet Number ◽  
Ray Theory ◽  
Péclet Number ◽  
Convection Diffusion

scholarly journals Formulation of Low Peclet Number Based Grid Expansion Factor for the Solution of the Convection Diffusion Equation

2018 ◽  
Vol 8 (2) ◽  
pp. 2680-2684
Author(s):  
A. Abdullah
Keyword(s):  
Peclet Number ◽  
Computational Domain ◽  
Expansion Factor ◽  
Structured Decision Making ◽  
Péclet Number ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Flow Parameters ◽  
Dimensional Parameters ◽  
Logarithmic Relationship

Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.

Improving the Efficiency of the Nodal Integral Method With the Portable, Extensible Toolkit for Scientific Computation

2002 ◽  
Author(s):  
Allen J. Toreja ◽  
Rizwan-Uddin
Keyword(s):  
Diffusion Equation ◽  
Peclet Number ◽  
Integral Method ◽  
Time Dependent ◽  
Scientific Computation ◽  
Péclet Number ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Nodal Integral Method ◽  
Successive Over Relaxation

An existing implementation of the nodal integral method for the time-dependent convection-diffusion equation is modified to incorporate various PETSc (Portable, Extensible Toolkit for Scientific Computation) solver and preconditioner routines. In the modified implementation, the default iterative Gauss-Seidel solver is replaced with one of the following PETSc iterative linear solver routines: Generalized Minimal Residuals, Stabilized Biconjugate Gradients, or Transpose-Free Quasi-Minimal Residuals. For each solver, a Jacobi or a Successive Over-Relaxation preconditioner is used. Two sample problems, one with a low Peclet number and one with a high Peclet number, are solved using the new implementation. In all the cases tested, the new implementation with the PETSc solver routines outperforms the original Gauss-Seidel implementation. Moreover, the PETSc Stabilized Biconjugate Gradients routine performs the best on the two sample problems leading to CPU times that are less than half the CPU times of the original implementation.

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

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