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The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.
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Practical Kinetic Models for Dense Fluids.

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A new kinetic modeling approach separates particle interactions into local and nonlocal parts, creating a generic equation for complex fluids. This method resolves causality issues and enables efficient simulation of compressible nonideal fluids.

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Area of Science:

  • Computational fluid dynamics
  • Theoretical fluid mechanics
  • Statistical mechanics

Background:

  • Kinetic models are essential for simulating complex fluid systems.
  • Causality issues arise from temperature gradients and nonideal equations of state.
  • Existing models face challenges in efficiently handling nonideal fluid behavior.

Purpose of the Study:

  • To develop a novel kinetic modeling approach for complex fluids.
  • To resolve causality obstructions in kinetic theory.
  • To derive an efficient numerical method for compressible nonideal fluid simulation.

Main Methods:

  • Separation of local and nonlocal contributions to particle interaction.
  • Gauge invariance applied to the hydrodynamic limit.
  • Derivation from Enskog-Vlasov kinetic theory.

Main Results:

  • A generic kinetic equation for complex fluid systems is established.
  • Causality issues related to temperature and nonideal state are resolved.
  • A new lattice Boltzmann model for compressible nonideal fluids is derived.

Conclusions:

  • The proposed method offers a robust framework for kinetic modeling.
  • The derived lattice Boltzmann model is suitable for efficient numerical simulations.
  • This approach advances the simulation capabilities for nonideal fluid dynamics.