Multiphase particle-in-cell method

Key takeaways

Multiphase particle-in-cell method belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Multiphase particle-in-cell method to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Multiphase particle-in-cell method from memory before moving on to harder problems.

Reference excerpt

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and as a continuum. In the MP-PIC approach, the particle properties are mapped from the Lagrangian coordinates to an Eulerian grid through the use of interpolation functions. After evaluation of the continuum derivative terms, the particle properties are mapped back to the individual particles. This method has proven to be stable in dense particle flows, computationally efficient, and physically accurate. This has allowed the MP-PIC method to be used as particle-flow solver for the simulation of industrial-scale chemical processes involving particle-fluid flows.

History The multiphase particle-in-cell (MP-PIC) method was originally developed for a one-dimensional case in the mid-1990s by P.J. O'Rourke (Los Alamos National Laboratory), who also coined the term MP-PIC. Subsequent extension of the method to two-dimensions was performed by D.M. Snider and O'Rourke. By 2001, D.M. Snider had extended the MP-PIC method to full three-dimensions. Currently, the MP-PIC method is used in commercial software for the simulation of particle-fluid systems and also available in MFiX suite by NETL.

Method The MP-PIC method is described by the governing equations, interpolation operators, and the particle stress model.

Governing equations

Fluid phase The multiphase particle-in-cell method assumes an incompressible fluid phase with the corresponding continuity equation,

∂ θ f ∂ t + ∇ ⋅ ( θ f u f ) = 0 , {\displaystyle {\frac {\partial \theta _{f}}{\partial t}}+\nabla \cdot (\theta _{f}\mathbf {u} _{f})=0,}

where the θ f {\displaystyle \theta _{f}\;} is the fluid volume fraction and u f {\displaystyle \mathbf {u} _{f}} is the fluid velocity. Momentum transport is given by a variation of the Navier-Stokes equations where ρ f {\displaystyle \rho _{f}} is the fluid density, p {\displaystyle p} is the fluid pressure, and g {\displaystyle \mathbf {g} } is the body force vector (gravity).

∂ θ f u f ∂ t + ∇ ⋅ ( θ f u f u f ) = − ∇ p ρ f − F ρ f + θ f g {\displaystyle {\frac {\partial \theta _{f}\mathbf {u} _{f}}{\partial t}}+\nabla \cdot (\theta _{f}\mathbf {u} _{f}\mathbf {u} _{f})=-{\frac {\nabla p}{\rho _{f}}}-{\frac {\mathbf {F} }{\rho _{f}}}+\theta _{f}\mathbf {g} }

The laminar fluid viscosity terms, not included in the fluid momentum equation, can be included if necessary but will have a negligible effect on dense particle flow. In the MP-PIC method, the fluid motion is coupled with the particle motion through F {\displaystyle \mathbf {F} } , the rate of momentum exchange per volume between the fluid and particle phases. The fluid phase equations are solved using a finite volume approach.

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Worked examples

Example 1 — a first encounter with Multiphase particle-in-cell method

Start with the simplest possible case. Write down what Multiphase particle-in-cell method claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Multiphase particle-in-cell method before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Multiphase particle-in-cell method ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Multiphase particle-in-cell method

In research: Multiphase particle-in-cell method appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Multiphase particle-in-cell method in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Multiphase particle-in-cell method is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational fluid dynamics, Numerical differential equations, so understanding it makes those chapters shorter.
In everyday life: Look for Multiphase particle-in-cell method outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Multiphase particle-in-cell method in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Multiphase particle-in-cell method means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Multiphase particle-in-cell method out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Multiphase particle-in-cell method in simple terms?

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the…

Why does Multiphase particle-in-cell method matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Multiphase particle-in-cell method?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Multiphase particle-in-cell method.