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Related Concept Videos

Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
Diffusion01:21

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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
Boundary Layer Characteristics01:18

Boundary Layer Characteristics

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
Viscosity01:17

Viscosity

When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...
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Viscosity

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Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

Advections with significantly reduced dissipation and diffusion.

ByungMoon Kim1, Yingjie Liu, Ignacio Llamas

  • 1Georgia Institute of Technology, Atlanta, GA 30332-0760, USA. bmkim@cc.gatech.edu

IEEE Transactions on Visualization and Computer Graphics
|November 10, 2006
PubMed
Summary

Back and Forth Error Compensation and Correction (BFECC) enhances advection simulations by reducing dissipation and diffusion. This method improves accuracy and significantly minimizes volume loss in level set evolution and various fluid dynamics applications.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Computer graphics

Background:

  • Advection equations are fundamental in simulating fluid flow, smoke, and other dynamic phenomena.
  • Traditional numerical methods often suffer from dissipation and diffusion errors, degrading simulation accuracy.
  • Level set methods are widely used for interface tracking but can experience volume loss.

Purpose of the Study:

  • To introduce and evaluate Back and Forth Error Compensation and Correction (BFECC) for advection computations.
  • To demonstrate BFECC's effectiveness in reducing numerical dissipation and diffusion.
  • To show BFECC's benefits for level set evolution and various simulation scenarios.

Main Methods:

  • BFECC was implemented as a modification to first-order upwind and semi-Lagrangian advection schemes.
  • The method was applied to advection of velocity, smoke density, and images on uniform and adaptive grids, and triangulated surfaces.
  • Second-order accuracy in space and time was achieved with BFECC.

Main Results:

  • BFECC significantly reduced dissipation and diffusion across various advection tasks.
  • Application to level set evolution led to a substantial decrease in volume loss.
  • Simulations of smoke, bubbles in water, and complex water-solid-air interactions showed improved fidelity.
  • Dye advection using BFECC effectively visualized vector fields.

Conclusions:

  • BFECC is a simple yet powerful technique for improving the accuracy of advection simulations.
  • The method offers significant advantages for fluid dynamics, computer graphics, and interface computations.
  • BFECC provides a robust solution for mitigating common numerical errors in advection-driven simulations.