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

Navier–Stokes Equations01:28

Navier–Stokes Equations

551
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
551
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

85
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
85
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

1.0K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.0K
Velocity Potential01:20

Velocity Potential

393
In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
393
Typical Model Studies01:30

Typical Model Studies

380
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
380
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

361
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
361

You might also read

Related Articles

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

Sort by
Same author

Effect of Circadian Rhythm Modulated Blood Flow on Nanoparticle based Targeted Drug Delivery in Virtual <i>In Vivo</i> Arterial Geometries.

bioRxiv : the preprint server for biology·2024
Same author

Modeling of spatiotemporal dynamics of ligand-coated particle flow in targeted drug delivery processes.

Proceedings of the National Academy of Sciences of the United States of America·2024
Same author

Variational coupling of non-matching discretizations across finitely deforming fluid-structure interfaces.

International journal for numerical methods in fluids·2023
Same author

Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations.

Computational mechanics·2023
Same author

Blood-Artery Interaction in Calcified Aortas and Abdominal Aortic Aneurysms.

Extreme Mechanics Letters·2022
Same author

Weakly imposed boundary conditions for shear-rate dependent non-Newtonian fluids: application to cardiovascular flows.

Mathematical biosciences and engineering : MBE·2021

Related Experiment Video

Updated: Jul 17, 2025

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.5K

A Variational Multiscale method with immersed boundary conditions for incompressible flows.

Soonpil Kang1, Arif Masud1

  • 1Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

Meccanica
|September 1, 2023
PubMed
Summary

This study introduces a new stabilized Navier-Stokes method for fluid dynamics simulations. It accurately models boundary layers around immersed objects using a parameter-free approach derived from the Variational Multiscale method.

Keywords:
Immersed boundaryIncompressible fluidsInterfacial stabilizationVariational Multiscale methodWeakly imposed essential boundary conditions

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.5K
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

3.9K

Related Experiment Videos

Last Updated: Jul 17, 2025

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.5K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.5K
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

3.9K

Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Fluid Mechanics

Background:

  • Incompressible Navier-Stokes equations are fundamental in fluid dynamics.
  • Accurate enforcement of Dirichlet boundary conditions at immersed boundaries is challenging.
  • Existing methods often require user-defined parameters or struggle with complex geometries.

Purpose of the Study:

  • To develop a novel stabilized formulation of the incompressible Navier-Stokes equations.
  • To enable weak enforcement of Dirichlet boundary conditions at immersed boundaries.
  • To create a parameter-free stabilization method for robust fluid simulations.

Main Methods:

  • Derivation of boundary terms using the Variational Multiscale (VMS) method.
  • Local solution of fine-scale variational problems near boundaries.
  • Variational embedding of the fine-scale model into the coarse-scale formulation.
  • Implementation with quadrilateral and hexahedral finite elements.

Main Results:

  • A stabilized method free of user-defined parameters was developed.
  • The method naturally incorporates area-averaging and stress-averaging properties.
  • Numerical simulations using 2D and 3D benchmark problems demonstrated robustness and accuracy.
  • Effective modeling of boundary layers around immersed objects was achieved.

Conclusions:

  • The proposed method provides a mathematically robust and computationally stable approach.
  • It accurately captures fluid behavior near immersed boundaries, even when misaligned with the mesh.
  • This work advances numerical techniques for complex fluid flow problems.