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Related Experiment Video

Updated: Jun 6, 2026

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

Fast and Robust Sixth Order Multigrid Computation for 3D Convection Diffusion Equation.

Yin Wang¹, Jun Zhang

¹Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA, URL: http://www.csr.uky.edu/~ywangf.

Journal of Computational and Applied Mathematics

|December 15, 2010

Summary

A new sixth order compact scheme accurately solves 3D convection diffusion equations. This numerical method enhances accuracy for high Reynolds number flows, outperforming existing fourth order schemes.

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The Diffusion of Passive Tracers in Laminar Shear Flow

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A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

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The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Area of Science:

Computational Fluid Dynamics
Numerical Analysis
Partial Differential Equations

Background:

Convection diffusion equations are crucial for modeling fluid flow phenomena.
Existing numerical schemes often struggle with accuracy at high Reynolds numbers.
A need exists for higher-order accurate methods for complex flow simulations.

Purpose of the Study:

To develop and validate a sixth order explicit compact finite difference scheme.
To solve the three-dimensional convection diffusion equation efficiently and accurately.
To improve grid-independent convergence rates for high Reynolds number flows.

Main Methods:

Employed a multiscale multigrid method with a 19-point fourth order discretization.
Utilized an operator-based interpolation and extrapolation technique for sixth order accuracy.
Implemented a plane relaxation smoother within the multigrid solver for enhanced grid independency.

Main Results:

The sixth order compact scheme (SOC) demonstrated superior accuracy compared to the fourth order compact scheme (FOC).
The plane relaxation smoother improved grid-independent convergence rates for high Reynolds number simulations.
Numerical results confirmed the efficiency and accuracy of the proposed SOC scheme.

Conclusions:

The developed sixth order compact scheme offers a significant improvement for solving 3D convection diffusion equations.
The method is particularly effective for high Reynolds number flows where traditional schemes falter.
This work provides a more accurate and reliable numerical tool for computational fluid dynamics research.