Practice Consistency (6.3) - Computational fluid dynamics (Contd.) - Hydraulic Engineering - Vol 3

Practice: Consistency

Lesson 6.3Computational fluid dynamics (Contd.)

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
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6 sample questions

Question 1.
Define consistency in numerical methods.
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Think about how numerical values should relate to the actual mathematical problem.
Question 2.
What is truncation error?
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Consider how approximations differ from exact solutions.
3Question 3.
What does consistency ensure in a numerical method?
- The method is accurate
- Errors diminish when grid size decreases
- Computational efficiency
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Consider how numerical methods should behave as the grid is refined.
4Question 4.
True or False: Convergence means the numerical solution approaches the exact solution for each independent variable.
- True
- False
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Focus on the definition of convergence in your studies.
Question 5.
Using von Neumann stability analysis, derive the conditions for stability in the explicit scheme for heat equation.
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Focus on how the discretization affects the stability of the numerical solution.
Question 6.
Construct a numerical example illustrating the consistency error associated with a first-order finite difference approximation.
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Identify the order of approximation and how it affects accuracy.

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