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Related Concept Videos

Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
Navier–Stokes Equations01:28

Navier–Stokes Equations

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...
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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:

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Related Experiment Video

Updated: May 9, 2026

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis
09:36

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

A meshless boundary method for Stokes flows with particles: application to canalithiasis.

F Boselli1, D Obrist, L Kleiser

  • 1Institute of Fluid Dynamics, ETH Zurich, 8092 Zurich, Switzerland.

International Journal for Numerical Methods in Biomedical Engineering
|July 16, 2013
PubMed
Summary

We developed a new meshless computational fluid dynamics method for low Reynolds number flows with particles. This efficient approach accurately simulates fluid dynamics, including conditions like canalithiasis.

Keywords:
BPPVStokes flowcanalithiasisendolymph flowforce coupling methodmultilayer MFSparticle-driven flow

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Last Updated: May 9, 2026

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Visualizing Cytoplasmic Flow During Single-cell Wound Healing in Stentor coeruleus

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Area of Science:

  • Computational fluid dynamics
  • Biophysics
  • Medical physics

Background:

  • Simulating fluid dynamics with finite-size particles at low Reynolds numbers presents computational challenges.
  • Existing methods often require complex meshing or extensive computational resources.

Purpose of the Study:

  • To develop an efficient, easy-to-program, and meshless computational method for low Reynolds number flows with finite-size particles.
  • To improve the computational efficiency of coupling the Method of Fundamental Solutions (MFS) with the Force Coupling Method (FCM).

Main Methods:

  • Coupling the Method of Fundamental Solutions (MFS) with the Force Coupling Method (FCM).
  • Extending the flow domain across the solid particle phase.
  • Approximating flow using a superposition of singular Stokeslets and finite-size multipoles.
  • Developing new MFS quadratures for efficient computation of volume integrals in FCM.

Main Results:

  • The proposed coupled MFS-FCM method is efficient and meshless for low Reynolds number flows.
  • New MFS quadratures provide exact computation of volume integrals, avoiding expensive Stokeslet evaluations.
  • The method is applicable to complex fluid dynamics problems, such as the fluid dynamics of canalithiasis.

Conclusions:

  • The coupled MFS-FCM method offers a significant advancement in simulating fluid dynamics with finite-size particles.
  • The developed MFS quadratures enhance computational efficiency.
  • This method provides a valuable tool for investigating pathologies like canalithiasis.