Practice Classification Problem (6.7) - Computational fluid dynamics (Contd.)

Practice: Classification Problem

Lesson 6.7Computational fluid dynamics (Contd.)

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What type of PDE is represented when m < 1?
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Refer back to the classifications we discussed.
Question 2.
Define consistency in the context of numerical methods.
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Think about how approximations relate to the true equation.
3Question 3.
What occurs when m is greater than 1 in the velocity potential equation?
- Elliptic
- Hyperbolic
- Parabolic
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Recall the behavior classifications for different m values.
4Question 4.
True or False: Consistency means that numerical solutions will closely approach the exact PDE solution.
- True
- False
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Think about the definitions we discussed in class.
Question 5.
Given the velocity potential equation classification: Analyze the behavior of the equation when m is close to zero, and predict the flow properties.
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Reflect on how small values of m affect the classifications.
Question 6.
Derive the condition αΔt/Δx² ≤ ½ for stability and explain its significance regarding numerical simulations.
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Think about how stability relates to error growth in the numerical method.

4 more questions in this section. Enroll free to practise them all.