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

Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

528
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
528
Navier–Stokes Equations01:28

Navier–Stokes Equations

594
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...
594
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.0K
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...
1.0K
Thermal expansion and Thermal stress: Problem Solving01:27

Thermal expansion and Thermal stress: Problem Solving

1.2K
San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in...
1.2K
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

345
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
345
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

375
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...
375

You might also read

Related Articles

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

Sort by
Same author

Comment on Sakaki et al. From Disease Staging to Early Graft Assessment in β-Cell Replacement Therapy.

Diabetes·2026
Same author

Dipole moment-induced asymmetric charge distribution of Fe atomic sites to boost photocatalytic hydrogen evolution.

Journal of colloid and interface science·2026
Same author

Neurophysiological Markers of Cancer-Related Fatigue Derived from High-Density EEG.

Brain topography·2025
Same author

Association between cumulative blood pressure and the risk of cognitive impairment in Chinese older adults: a longitudinal study over 16 years.

BMC geriatrics·2025
Same author

NDRG2 regulates milkfatbiosynthesis by targeting the AMPK/SREBP1 axis in bovine mammary epithelial cells.

International journal of biological macromolecules·2025
Same author

Quantitative assessment method for firefighting danger based on numerical simulation of forest fire spread in canyon wind fields.

PloS one·2025

Related Experiment Video

Updated: Jul 24, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.6K

A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations.

Xianzhu Li1, Haiyan Su1

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

Entropy (Basel, Switzerland)
|July 8, 2023
PubMed
Summary

A new grad-div stabilization algorithm enhances computational efficiency for magnetohydrodynamic (MHD) equations. This method improves stability and convergence, outperforming existing approaches in numerical experiments.

Keywords:
modular grad-div stabilizationoptimal convergencestabilitythermally coupled MHD

More Related Videos

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

481
Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

6.6K

Related Experiment Videos

Last Updated: Jul 24, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.6K
Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

481
Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

6.6K

Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Plasma Physics

Background:

  • Time-dependent, thermally coupled magnetohydrodynamic (MHD) equations present significant computational challenges.
  • Existing numerical methods often struggle with stability and efficiency, particularly at higher Reynolds numbers.
  • Divergence errors in velocity fields can degrade solution accuracy and stability in MHD simulations.

Purpose of the Study:

  • To introduce a fully discrete modular grad-div stabilization algorithm for time-dependent, thermally coupled MHD equations.
  • To enhance computational efficiency and stability, especially for increasing Reynolds numbers and stabilization parameters.
  • To provide rigorous mathematical analysis of the algorithm's stability and convergence properties.

Main Methods:

  • Development of a minimally intrusive modular component to penalize velocity divergence errors.
  • Implementation of a fully discrete numerical scheme for the coupled MHD system.
  • Theoretical analysis to prove unconditional stability and optimal convergence rates.

Main Results:

  • The proposed grad-div stabilization algorithm demonstrates unconditional stability.
  • Optimal convergence rates are proven for the numerical scheme.
  • Numerical experiments confirm improved computational efficiency and accuracy compared to methods without grad-div stabilization.

Conclusions:

  • The novel grad-div stabilization algorithm offers a robust and efficient approach for simulating MHD phenomena.
  • The method effectively mitigates divergence errors, leading to more accurate and stable simulations.
  • This algorithm represents a significant advancement for computational studies involving MHD equations.