Related Experiment Video
Updated: Mar 6, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows
Andreas Krämer1, Knut Küllmer1, Dirk Reith1
1Institute for Technology, Renewables and Energy-efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany.
Physical Review. E
|March 17, 2017
Summary
This study enhances the lattice Boltzmann method (LBM) for computational fluid dynamics. The new semi-Lagrangian streaming step enables larger time steps and unstructured grids for more accurate fluid simulations.
Area of Science:
- Computational fluid dynamics
- Numerical methods
Background:
- The standard lattice Boltzmann method (LBM) is limited to regular grids and a Courant-Friedrichs-Lewy (CFL) number of one.
- These limitations restrict its application in complex fluid flow simulations.
Purpose of the Study:
- To advance the standard LBM by incorporating a semi-Lagrangian streaming step.
- To overcome the limitations of regular grids and unity CFL number in LBM.
Main Methods:
- Introduction of a semi-Lagrangian streaming step into the LBM.
- Development of a modified LBM capable of handling unstructured grids and higher-order accuracy.
Main Results:
- The enhanced LBM allows for significantly larger time steps compared to the standard method.
- The approach supports the use of unstructured grids, offering greater flexibility.
- Higher-order accurate solutions were achieved in simulations.
Conclusions:
- The semi-Lagrangian streaming step significantly improves the flexibility and accuracy of the LBM.
- The modified LBM is effective for simulating complex fluid dynamics problems, including vortex dynamics and shear layers.
Related Concept Videos
01:22Eulerian and Lagrangian Flow Descriptions
2.1K
Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
2.1K
01:07Laminar and Turbulent Flow
11.3K
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
11.3K
01:17Steady, Laminar Flow Between Parallel Plates
936
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.
936
01:30Bernoulli's Equation for Flow Along a Streamline
1.6K
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:
1.6K
01:20Maxwell-Boltzmann Distribution: Problem Solving
3.1K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
3.1K
01:28Navier–Stokes Equations
2.5K
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...
2.5K