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

You might also read

Related Articles

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

Sort by
Same author

Equilibrium-distribution-function-based mesoscopic finite-difference methods for partial differential equations: Modeling and analysis.

Physical review. E·2026
Same author

Identification and regulatory mechanism analysis of macrophage-related key genes in diabetic nephropathy.

Diabetology & metabolic syndrome·2026
Same author

Molecular Insights into the Regulatory Mechanisms Mediated by Hypoxia-Conditioned Skeletal Muscle Exosomal miRNAs.

Biomarker insights·2026
Same author

Phase-field-based lattice Boltzmann method for the transport of insoluble surfactant in two-phase flows.

Physical review. E·2025
Same author

Endoscopic retrograde cholangiopancreatography combined with peroral choledochoscope for the treatment of complete bile duct rupture.

Endoscopy·2025
Same author

Phase-field-based lattice Boltzmann method for containerless freezing.

Physical review. E·2024

Related Experiment Video

Updated: Jun 30, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method.

Xi Liu1, Ying Chen1, Zhenhua Chai1,2,3

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.

Physical Review. E
|March 16, 2024
PubMed
Summary
This summary is machine-generated.

A new macroscopic finite-difference scheme derived from the regularized lattice Boltzmann (RLB) method offers efficient and accurate solutions for the Navier-Stokes equations (NSEs) and convection-diffusion equation (CDE). This method simplifies computations by using macroscopic variables, achieving second-order spatial accuracy.

More Related Videos

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

12.8K
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

Related Experiment Videos

Last Updated: Jun 30, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K
Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

12.8K
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

Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Mesoscopic and macroscopic modeling

Background:

  • The regularized lattice Boltzmann (RLB) method is a mesoscopic approach for solving fluid dynamics and transport equations.
  • Common RLB methods rely on the evolution of distribution functions, which can be computationally intensive and memory-demanding.
  • Developing efficient and accurate numerical schemes for the Navier-Stokes equations (NSEs) and convection-diffusion equation (CDE) remains a key challenge.

Purpose of the Study:

  • To develop a macroscopic finite-difference scheme derived from the mesoscopic RLB method.
  • To solve the Navier-Stokes equations (NSEs) and convection-diffusion equation (CDE) using this new scheme.
  • To demonstrate the scheme's efficiency, accuracy, and simplicity compared to existing methods.

Main Methods:

  • A macroscopic finite-difference scheme was developed from the mesoscopic regularized lattice Boltzmann (RLB) method.
  • The scheme utilizes hydrodynamic variables (density, momentum, strain rate tensor) for NSEs and macroscopic variables (concentration, flux) for CDE.
  • A second-order accuracy in space was established through theoretical analysis.

Main Results:

  • The developed macroscopic scheme exhibits low memory requirements and high computational efficiency.
  • Numerical simulations of benchmark problems show excellent agreement with analytical solutions.
  • The scheme achieves second-order accuracy in space, consistent with the mesoscopic RLB method.

Conclusions:

  • The new macroscopic finite-difference scheme offers a simpler and more efficient alternative to the RLB method and its equivalent macroscopic schemes.
  • The scheme is a two-level system using macroscopic variables, enhancing computational performance.
  • The findings validate the scheme's accuracy and efficiency for solving NSEs and CDE.