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

Typical Model Studies01:30

Typical Model Studies

360
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.
360
Conservation of Mass in Finite Cotrol Volume01:16

Conservation of Mass in Finite Cotrol Volume

1.3K
The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
1.3K
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

946
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
946
Control Volume and System Representations01:16

Control Volume and System Representations

1.2K
Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
The control volume approach considers a stationary region in space through which fluid flows. This region is bounded by a control surface.  For instance, in the case of water...
1.2K
Boundary Layer Characteristics01:18

Boundary Layer Characteristics

125
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...
125
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

199
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.
199

You might also read

Related Articles

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

Sort by
Same author

Metagenomic analysis of the community structure and functional potential of <i>Tamarix</i> rhizosphere microbiomes along a soil salinity gradient.

Frontiers in microbiology·2026
Same author

Stabilized Radial Basis Function Finite Difference Schemes with Mass Conservation for the Cahn-Hilliard Equation on Surfaces.

Entropy (Basel, Switzerland)·2025
Same author

Corrigendum to "Caveolin-1-deficient fibroblasts promote migration, invasion, and stemness by activating the TGF-β/Smad signaling pathway in breast cancer cells".

Acta biochimica et biophysica Sinica·2025
Same author

Biocontrol potential of borrelidin metabolites derived from Streptomyces rochei A144 as a fungicide.

Journal of applied microbiology·2025
Same author

Bioprospecting of a Native Plant Growth-Promoting Bacterium <i>Bacillus cereus</i> B6 for Enhancing Uranium Accumulation by Sudan Grass (<i>Sorghum sudanense</i> (Piper) Stapf).

Biology·2025
Same author

How can we improve the successful identification of patients suitable for CAR-T cell therapy?

Expert review of molecular diagnostics·2024

Related Experiment Video

Updated: Jul 7, 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

3.9K

Modified Characteristic Finite Element Method with Second-Order Spatial Accuracy for Solving Convection-Dominated

Longyuan Wu1, Xinlong Feng1, Yinnian He1,2

  • 1College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China.

Entropy (Basel, Switzerland)
|December 23, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel finite element method for solving surface-based convection-reaction-diffusion equations. The modified method achieves second-order accuracy, improving upon existing techniques for complex surface simulations.

Keywords:
Taylor expansionexplicit–implicit methodstabilitysurface convection–reaction–diffusion equationssurface finite element

More Related Videos

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.5K
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

1.9K

Related Experiment Videos

Last Updated: Jul 7, 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

3.9K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.5K
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

1.9K

Area of Science:

  • Numerical Analysis
  • Computational Mathematics
  • Surface Geometry

Background:

  • Convection-reaction-diffusion equations are crucial in modeling phenomena on curved surfaces.
  • Existing numerical methods often struggle with accuracy and stability on surfaces.
  • Characteristic finite element methods offer a promising approach but require refinement for surface applications.

Purpose of the Study:

  • To develop a modified characteristic finite element method (FEM) for second-order accurate spatial solutions.
  • To address the unique challenges of solving equations on surfaces, where characteristic paths are constrained.
  • To enhance the stability and effectiveness of numerical schemes for surface-based PDEs.

Main Methods:

  • Employed a backward-Euler method for temporal discretization.
  • Utilized a surface finite element method for spatial discretization.
  • Applied Taylor expansion to accurately approximate solutions along characteristic directions on the surface.

Main Results:

  • Achieved second-order spatial accuracy for the numerical scheme.
  • Demonstrated the stability of the proposed method through mathematical proof.
  • Showcased the method's effectiveness via numerical examples and comparison with existing techniques.

Conclusions:

  • The modified characteristic FEM provides a robust and accurate solution for convection-reaction-diffusion equations on surfaces.
  • The Taylor expansion-based reconstruction is vital for handling characteristic directions on surfaces.
  • This method offers a significant improvement over existing face mesh-based characteristic FEMs.