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Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

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Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
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Laminar Flow: Problem Solving01:24

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Newtonian Fluid: Problem Solving01:18

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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Fast Decoupled and DC Powerflow01:24

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The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Updated: Nov 29, 2025

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
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High-order kinetic flow solver based on the flux reconstruction framework.

Ji Li1, Chengwen Zhong1, Sha Liu1

  • 1National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.

Physical Review. E
|November 20, 2020
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Summary

This study introduces a high-order numerical method combining the kinetic inviscid flux (KIF) and flux reconstruction (FR) frameworks. This approach balances the benefits of gas-kinetic schemes with reduced computational costs, showing promise for simulating turbulent flows.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Gas Kinetic Theory

Background:

  • The gas-kinetic scheme (GKS) offers excellent merits but can be computationally expensive.
  • Existing numerical frameworks require methods that balance accuracy with efficiency.
  • Integrating advanced kinetic theories into established numerical schemes is an ongoing challenge.

Purpose of the Study:

  • To develop a high-order numerical method using the kinetic inviscid flux (KIF) and flux reconstruction (FR) frameworks.
  • To create a method that retains the advantages of the gas-kinetic scheme (GKS) while reducing computational costs.
  • To enhance the efficiency of numerical simulations based on gas-kinetic theory.

Main Methods:

  • Developed a novel numerical method by integrating the kinetic inviscid flux (KIF) with the flux reconstruction (FR) framework.
  • KIF combines the totally thermalized transport (TTT) scheme and kinetic flux vector splitting (KFVS) method.
  • Replaced the Riemann flux solver at element interfaces with the KIF method, computing common solutions based on gas-kinetic theory.

Main Results:

  • The combined KIF-FR method demonstrated accuracy and efficiency in numerical simulations.
  • Adaptive weighting of TTT and KFVS fluxes was achieved using a coefficient related to time step and collision time.
  • The Taylor-Green vortex problem was used to validate the method's capability in simulating turbulent flows.

Conclusions:

  • The KIF-FR method provides a robust, efficient, and accurate high-order numerical approach.
  • The integration of gas-kinetic theory principles into the FR framework is feasible and beneficial.
  • The developed method shows significant potential for simulating complex fluid dynamics problems, including turbulence.