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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Elastic Collisions: Introduction01:00

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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
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Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
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Types of Collisions - II01:19

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When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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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).
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Lattice Centering and Coordination Number02:33

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Related Experiment Videos

Machine-learning-enhanced collision operator for the lattice Boltzmann method based on invariant networks.

Mario Christopher Bedrunka1, Tobias Horstmann2, Ben Picard3

  • 1Bonn-Rhein-Sieg University of Applied Sciences, University of Siegen, Chair of Fluid Mechanics, Paul-Bonatz-Straße 9-11, 57076 Siegen-Weidenau, Germany and Institute of Technology, Resource and Energy-efficient Engineering (TREE), Grantham-Allee 20, 53757 Sankt Augustin, Germany.

Physical Review. E
|December 23, 2025
PubMed
Summary
This summary is machine-generated.

Machine learning enhances computational fluid dynamics simulations by optimizing the lattice Boltzmann method

Related Experiment Videos

Area of Science:

  • Computational fluid dynamics
  • Machine learning
  • Numerical simulations

Background:

  • The lattice Boltzmann method (LBM) is a numerical solver for fluid dynamics.
  • Integrating machine learning (ML) into LBM can improve accuracy and stability.
  • The collision operator is a key component for ML integration in LBM.

Purpose of the Study:

  • To develop a novel neural collision operator (NCO) for LBM.
  • To enhance the robustness and accuracy of LBM simulations using ML.
  • To optimize relaxation rates of nonphysical moments for improved stability.

Main Methods:

  • Constructed an invariant neural network acting on an equivariant collision operator.
  • Trained the NCO using forced isotropic turbulence simulations with spectral forcing.
  • Minimized energy spectrum discrepancy and tailored numerical dissipation via a custom loss function.

Main Results:

  • The NCO demonstrated improved accuracy and stability compared to BGK and KBC operators.
  • Accurate prediction of dynamics in highly underresolved three-dimensional Taylor-Green vortex (TGV) flows.
  • Robust performance in turbulent three-dimensional cylinder flow simulations.

Conclusions:

  • The NCO offers a promising approach for enhancing LBM simulations.
  • ML integration in LBM collision operators leads to more accurate and stable results.
  • Alternative training procedures enable high Reynolds number simulations with reduced memory footprint.