OpenFOAM多相流解析

Category: 解析 | Integrated 2026-04-06
CAE visualization for openfoam multiphase theory - technical simulation diagram
OpenFOAM多相流解析

Theory and Physics

Overview

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Teacher! Today's topic is about OpenFOAM multiphase flow analysis, right? What is it like?


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Analyzes free surface, dispersed systems, and reactive multiphase flows using solvers like interFoam (VOF Method), multiphaseInterFoam, reactingMultiphaseEulerFoam, etc. Interface capturing via the MULES algorithm.


🧑‍🎓

Teacher's explanation is easy to understand! The haze around free surface etc. with those solvers has cleared up.


Governing Equations


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Expressing this with equations, it looks like this.


$$\frac{\partial\alpha}{\partial t} + \nabla\cdot(\mathbf{U}\alpha) + \nabla\cdot(\mathbf{U}_r\alpha(1-\alpha)) = 0$$

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Hmm, just the equation doesn't quite click... What does it represent?


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CSF model for surface tension:



$$\mathbf{f}_\sigma = \sigma\kappa\nabla\alpha, \quad \kappa = -\nabla\cdot\hat{\mathbf{n}}$$
🧑‍🎓

Teacher's explanation is easy to understand! The haze around surface tension has cleared up.


Theoretical Foundation

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I've heard of "theoretical foundation," but I might not fully understand it...


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The numerical methods for OpenFOAM multiphase flow analysis are based on the Finite Volume Method (FVM) or the Finite Element Method (FEM). Being open source, its greatest advantage is the ability to verify and modify algorithm details at the source code level. Discretization schemes and convergence criteria logic, which are black boxes in commercial solvers, can be directly examined, making it particularly suitable for academic research and method development. Continuous improvement and bug fixes by the community ensure quality.


🧑‍🎓

Ah, I see! So that's how the numerical methods for multiphase flow analysis work.


Theoretical Background of Numerical Methods

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Teacher, please teach me about the "theoretical background of numerical methods"!


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Explains the theoretical foundation of numerical methods implemented by open-source CAE tools.



Variational Principle of the Finite Element Method (FEM)

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Please teach me about the "Finite Element Method"!


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The principle of minimum potential energy, fundamental to structural analysis:



$$ \Pi(\mathbf{u}) = \frac{1}{2} \int_{\Omega} \boldsymbol{\sigma} : \boldsymbol{\varepsilon} \, d\Omega - \int_{\Omega} \mathbf{f} \cdot \mathbf{u} \, d\Omega - \int_{\Gamma_t} \mathbf{t} \cdot \mathbf{u} \, d\Gamma $$


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The displacement field $\mathbf{u}$ that makes $\Pi$ stationary is the equilibrium solution. CalculiX and Code_Aster implement the Galerkin method based on this variational principle.




Conservation Law of the Finite Volume Method (FVM)

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Please teach me about the "Finite Volume Method"!


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The FVM adopted by OpenFOAM is based on the integral conservation law for a control volume:



$$ \frac{\partial}{\partial t} \int_{V} \rho \phi \, dV + \oint_{S} \rho \phi \mathbf{u} \cdot d\mathbf{S} = \oint_{S} \Gamma \nabla \phi \cdot d\mathbf{S} + \int_{V} S_\phi \, dV $$


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Discrete equations are obtained by applying this integral form to each control volume and numerically evaluating the fluxes on the faces.



License and Quality Assurance

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Please teach me about "License and Quality Assurance"!


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Open-source CAE allows third-party verification of algorithms because the source code is public. On the other hand, there is no vendor support like with commercial tools, making information sharing within user communities and forums crucial.



Application Conditions and Precautions

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I've heard of "Application Conditions and Precautions," but I might not fully understand it...


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  • Results from OSS tools should always be validated against known benchmark problems.
  • Be aware of version incompatibilities (especially differences between OpenFOAM forks).
  • It is recommended to verify OSS accuracy by comparing results with commercial tools.
  • When documentation is lacking, direct reference to the source code may be necessary.

🧑‍🎓

So, cutting corners on tool results will come back to bite you later. I'll keep that in mind!


Dimensionless Parameters and Dominant Scales

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Teacher, please teach me about "Dimensionless Parameters and Dominant Scales"!


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Understanding the dimensionless parameters governing the physical phenomenon being analyzed is fundamental to appropriate model selection and parameter setting.


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  • Peclet Number Pe: Relative importance of convection vs. diffusion. Pe >> 1 indicates convection dominance (stabilization techniques required).
  • Reynolds Number Re: Ratio of inertial to viscous forces. Fundamental parameter for fluid problems.
  • Biot Number Bi: Ratio of internal conduction to surface convection. Bi < 0.1 allows application of the lumped capacitance method.
  • Courant Number CFL: Indicator of numerical stability. Explicit methods require CFL ≤ 1.

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Ah, I see! So that's how the physical phenomenon being analyzed works.



Verification via Dimensional Analysis

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Please teach me about "Verification via Dimensional Analysis"!


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Dimensional analysis based on Buckingham's Π theorem is effective for order-of-magnitude estimation of analysis results. Using characteristic length $L$, characteristic velocity $U$, and characteristic time $T = L/U$, estimate the order of each physical quantity beforehand to confirm the validity of the analysis results.


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I see. So if you can handle the physical phenomenon being analyzed, you're basically okay to start?


Classification and Mathematical Characteristics of Boundary Conditions

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I've heard that if you mess up the boundary conditions, everything goes wrong...


TypeMathematical ExpressionPhysical MeaningExample
Dirichlet Condition$u = u_0$ on $\Gamma_D$Specification of variable valueFixed wall, specified temperature
Neumann Condition$\partial u/\partial n = g$ on $\Gamma_N$Specification of gradient (flux)Heat flux, force
Robin Condition$\alpha u + \beta \partial u/\partial n = h$Linear combination of variable and gradientConvective heat transfer
Periodic Boundary Condition$u(x) = u(x+L)$Spatial periodicityUnit cell analysis
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Choosing appropriate boundary conditions is directly linked to solution uniqueness and physical validity. Insufficient boundary conditions lead to an ill-posed problem, while excessive ones cause contradictions.



🧑‍🎓

I've grasped the overall picture of OpenFOAM multiphase flow analysis! I'll try to be mindful of it in my practical work starting tomorrow.


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Yeah, you're doing great! Actually getting hands-on is the best way to learn. If you don't understand something, feel free to ask anytime.


Coffee Break Casual Talk

Is the Interface "Thickness" Zero or Non-Zero?—Physical Interpretation of the VOF Method

In the VOF (Volume of Fluid) method used by OpenFOAM's interFoam, the gas-liquid interface is represented as a "region where the volume fraction α changes from 0 to 1." Physically, the interface thickness is at the molecular scale (nanometers), but at CFD mesh cell sizes (millimeters to centimeters), the interface must be treated as a "diffused transition layer." The interfacialCompression (α compression term) incorporated into interFoam's alpha.water equation suppresses this artificial interface diffusion. There is a trade-off between interface "sharpness" and "numerical stability"; increasing the compressionFactor cAlpha from 1.0 to 2.0 makes the interface clearer but increases numerical oscillations. This single setting significantly influences calculation quality—a delicate balance between physics and numerics.

Physical Meaning of Each Term
  • Time Derivative of Conserved Quantity: Represents the rate of change over time of the physical quantity in question. Becomes zero for steady-state problems. 【Image】When filling a bathtub with hot water, the water level rises over time—this "rate of change per time" is the time derivative. The state where the valve is closed and the water level is constant is "steady," and the time derivative is zero.
  • Flux Term (Flow Term): Describes the spatial transport/diffusion of the physical quantity. Broadly classified into convection and diffusion. 【Image】Convection is like "a river's current carrying a boat," where things are carried by the flow. Diffusion is like "ink naturally spreading in still water," where things move due to concentration differences. The competition between these two transport mechanisms governs many physical phenomena.
  • Source Term (Generation/Destruction Term): Represents the local generation or destruction of the physical quantity, such as external forces or reaction terms. 【Image】Turning on a heater in a room "generates" thermal energy at that location. Fuel consumption in a chemical reaction "destroys" mass. A term representing physical quantities injected into the system from the outside.
Assumptions and Applicability Limits
  • The continuum assumption must hold for the spatial scale.
  • The constitutive laws of materials/fluids (stress-strain relationship, Newtonian fluid law, etc.) must be within their applicable range.
  • Boundary conditions must be physically reasonable and mathematically well-defined.
Dimensional Analysis and Unit Systems
VariableSI UnitNotes / Conversion Memo
Characteristic Length $L$mMust match the unit system of the CAD model.
Characteristic Time $t$sTime step for transient analysis should consider CFL condition and physical time constants.

Numerical Methods and Implementation

Details of Numerical Methods

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Specifically, what algorithms are used to solve OpenFOAM multiphase flow analysis?


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Explains key points of numerical methods and implementation for OpenFOAM multiphase flow analysis.



Compilation and Build

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I've heard of "Compilation and Build," but I might not fully understand it...


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Building from source code uses CMake or dedicated build systems (like OpenFOAM's wmake). Proper version management of dependency libraries (MPI, PETSc, BLAS/LAPACK, etc.) is crucial. Linux environments are recommended, but using WSL2 or Docker containers makes it possible on Windows as well.


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So, cutting corners on building from source will come back to bite you later. I'll keep that in mind!

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