Related Experiment Video
Updated: Jun 2, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
A lattice Boltzmann approach for solving scalar transport equations
Raoyang Zhang1, Hongli Fan, Hudong Chen
1Exa Corporation, 55 Network Drive, Burlington, MA 01803, USA. raoyang@exa.com
Summary
A novel lattice Boltzmann (LB) method solves scalar transport equations using dual distribution functions. This approach ensures numerical stability and accurate conservation laws for scalar transport simulations.
Area of Science:
- Computational fluid dynamics
- Numerical methods
- Transport phenomena
Background:
- Scalar transport equations are crucial in various scientific and engineering fields.
- Existing numerical methods may face limitations in stability and accuracy.
- The lattice Boltzmann method is a powerful tool for simulating complex fluid flows.
Purpose of the Study:
- To develop a lattice Boltzmann (LB) approach for solving scalar transport equations.
- To introduce a robust and efficient numerical method for scalar transport.
- To demonstrate the applicability of LB methods beyond fluid flow simulations.
Main Methods:
- A second set of distribution functions is introduced for transport scalars within the LB framework.
- The method fully recovers the macroscopic scalar transport equation.
- Generalized boundary conditions for arbitrary geometries are implemented.
Main Results:
- The LB approach satisfies exact conservation laws for scalar transport.
- Numerical stability is achieved without a Courant-Friedrichs-Lewy-like upper limit for scalar diffusivity.
- Solutions demonstrate independence from grid orientations with sufficient lattice isotropy.
- Accurate control of surface scalar flux enables generalized boundary conditions.
Conclusions:
- The presented LB approach offers an accurate, efficient, and robust solution for scalar transport equations.
- This method extends the applicability of LB methods to a wider range of transport phenomena.
- The numerical stability and grid independence make it suitable for complex geometries and simulations.
Related Concept Videos
01:21Carrier Transport
The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
01:20Maxwell-Boltzmann Distribution: Problem Solving
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
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
01:27Lattice Energies of Ionic Crystals
Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
01:24Reynolds Transport Theorem
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.