Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Laminar Flow: Problem Solving01:24

Laminar Flow: Problem Solving

Laminar flow occurs when a fluid moves smoothly in parallel layers with minimal mixing and turbulence. In fluid mechanics, ensuring laminar flow within a pipe is essential for precise control of flow characteristics, especially in engineering applications. The key factor in determining whether flow remains laminar is the Reynolds number, a dimensionless quantity that depends on the fluid's velocity, density, viscosity, and the pipe's diameter. A Reynolds number of 2100 or lower indicates...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PloS oneยท2017
See all related articles

Related Experiment Video

Updated: May 19, 2026

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches
10:58

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

Published on: July 22, 2025

The repeated replacement method: a pure Lagrangian meshfree method for computational fluid dynamics.

Wade A Walker1

  • 1wwalker3@austin.rr.com

Plos One
|August 7, 2012
PubMed
Summary

The repeated replacement method (RRM) is a novel meshfree approach for computational fluid dynamics (CFD). This method simulates fluid flow by adaptively replacing fluid cells, achieving high-resolution results with a unique mathematical framework.

More Related Videos

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

Related Experiment Videos

Last Updated: May 19, 2026

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches
10:58

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

Published on: July 22, 2025

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

Area of Science:

  • Computational Fluid Dynamics (CFD)
  • Meshfree Methods
  • Fluid Flow Simulation

Background:

  • Traditional CFD methods often rely on meshes, Riemann solvers, and numerical integration.
  • Simulating compressible fluid dynamics requires accurate modeling of density, velocity, and pressure evolution.
  • Adaptive accuracy is crucial for efficient computational fluid dynamics.

Purpose of the Study:

  • Introduce the Repeated Replacement Method (RRM), a novel meshfree technique for CFD.
  • Demonstrate RRM's ability to simulate fluid flow by modeling the tendency towards constant fluid properties.
  • Highlight RRM's adaptive accuracy and unique mathematical framework.

Main Methods:

  • RRM simulates fluid flow by repeatedly replacing fluid from active areas with new 'flattened' cells of equal mass, momentum, and energy.
  • The method adaptively adjusts the size and location of replaced fluid cells based on gradient magnitudes.
  • RRM operates in a purely Lagrangian mode without using meshes, stencils, Riemann solvers, or numerical derivatives.

Main Results:

  • RRM produces results comparable to high-resolution CFD methods on common test problems.
  • The adaptive cell replacement strategy naturally allocates computational effort to active fluid regions.
  • The method avoids traditional CFD components like Riemann solvers, flux limiters, and equation integration.

Conclusions:

  • RRM offers a distinct and effective meshfree alternative for computational fluid dynamics simulations.
  • The method's adaptive nature provides efficient and accurate simulations, particularly in regions of high fluid activity.
  • RRM's unique mathematical framework bypasses many conventional CFD computational techniques.