SIMPLEC algorithm

Key takeaways

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

Reference excerpt

The SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of SIMPLE algorithm; is a commonly used numerical procedure in the field of computational fluid dynamics to solve the Navier–Stokes equations. This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps as the SIMPLE algorithm, with the variation that the momentum equations are manipulated, allowing the SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. This modification attempts to minimize the effects of dropping velocity neighbor correction terms.

Algorithm The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. p*, u*, v* are guessed Pressure, X-direction velocity and Y-direction velocity respectively, p', u', v' are the correction terms respectively and p, u, v are the correct fields respectively; Φ is the property for which we are solving and d terms are involved with the under relaxation factor. So, steps are as follows: 1. Specify the boundary conditions and guess the initial values. 2. Determine the velocity and pressure gradients. 3. Calculate the pseudo velocities.

u ^ i , J = ∑ a n b u n b ∗ + b i , J a i , J {\displaystyle {\hat {u}}_{i,J}={\frac {\sum a_{nb}u_{nb}^{*}+b_{i,J}}{a_{i,J}}}}

v ^ I , j = ∑ a n b v n b ∗ + b I , j a I , j {\displaystyle {\hat {v}}_{I,j}={\frac {\sum a_{nb}v_{nb}^{*}+b_{I,j}}{a_{I,j}}}}

4. Solve for the pressure equation and get the p.

a I , J p I , J = a I − 1 , J p I − 1 , J + a I + 1 , J p I + 1 , J + a I , J − 1 p I , J − 1 + a I , J + 1 p I , J + 1 + b I , J {\displaystyle a_{I,J}p_{I,J}=a_{I-1,J}p_{I-1,J}+a_{I+1,J}p_{I+1,J}+a_{I,J-1}p_{I,J-1}+a_{I,J+1}p_{I,J+1}+b_{I,J}}

5. Set p*=p. 6. Using p* solve the discretized momentum equation and get u* and v*.

a i , J u i , J ∗ = ∑ a n b u n b ∗ + ( p I − 1 , J ∗ − p I , J ∗ ) A i , J + b i , J {\displaystyle a_{i,J}u_{i,J}^{*}=\sum a_{nb}u_{nb}^{*}+(p_{I-1,J}^{*}-p_{I,J}^{*})A_{i,J}+b_{i,J}}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with SIMPLEC algorithm

Start with the simplest possible case. Write down what SIMPLEC algorithm claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, 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 SIMPLEC algorithm 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 SIMPLEC algorithm 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 SIMPLEC algorithm

In research: SIMPLEC algorithm appears in computer science 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 SIMPLEC algorithm 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: SIMPLEC algorithm is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational fluid dynamics, so understanding it makes those chapters shorter.
In everyday life: Look for SIMPLEC algorithm 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 SIMPLEC algorithm in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what SIMPLEC algorithm 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 SIMPLEC algorithm out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is SIMPLEC algorithm in simple terms?

The SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of SIMPLE algorithm; is a commonly used numerical procedure in the field of computational fluid dynamics to solve the Navier–Stokes equations. This algorithm was developed by Van Doormal and Raith…

Why does SIMPLEC algorithm matter?

Because it connects several computer science 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 SIMPLEC algorithm?

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 SIMPLEC algorithm.