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.

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 Arterial pharmacokinetics in a patient-specific atherosclerotic artery-a simulation study

2021 ◽  
Vol 41 (1) ◽  
pp. 62-77
Author(s):  
Sayantan Biswas ◽  
- Sarifuddin ◽  
Prashanta Kumar Mandal
Keyword(s):  
Drug Delivery ◽  
Peclet Number ◽  
Numerical Study ◽  
Interface Roughness ◽  
Image Processing Technique ◽  
Patient Specific ◽  
Computational Domain ◽  
Péclet Number ◽  
Tissue Porosity ◽  
Near Wall

Of concern in the paper is a numerical study of endovascular drug delivery in a patient-specific atherosclerotic artery through a mathematical model in which the luminal flow is governed by an incompressible vis- cous Newtonian fluid, and the transport of luminal as well as tissue concentration is modeled as an unsteady convection-diffusion process. An image processing technique has been successfully adopted to detect the edges of the computational domain extracted from an asymmetric (about the centerline of the artery) patient-specific atherosclerotic artery. Considering each pixel as a control volume, the Marker and Cell (MAC) method has been leveraged to get a quantitative insight of the model considered by exploiting physiologically realistic initial, boundary as well as interface conditions. Simulated results reveal that the number as well as the length of separation zone does increase with increasing Re, and the near-wall velocity contour might be important for estimating the near-wall residence time for the pool of drug molecules available for tissue uptake. Results also show that the more the tissue porosity and interface roughness do not necessarily imply the more the effective- ness of delivery, even though they enhance the averaged concentration in the tissue domains, and also the area under concentration diminishes with increasing Peclet number. Thus, the tissue porosity, the Peclet number and various geometrical shapes (interface roughness) play a pivotal role in the dispersion and the effectiveness of drug delivery. GANITJ. Bangladesh Math. Soc.41.1 (2021) 62-77

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