Practice Convergence (6.4) - Computational fluid dynamics (Contd.) - Hydraulic Engineering - Vol 3

Practice: Convergence

Lesson 6.4Computational fluid dynamics (Contd.)

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10 questions

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6 sample questions

Question 1.
Define convergence in the context of numerical methods.
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Think about what 'approaching' means in mathematics.
Question 2.
What is discretization error?
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Consider what happens when you sample a continuous curve.
3Question 3.
What is convergence in numerical methods?
- A method's accuracy
- An approximation to a problem
- Approaching the exact solution as grid size decreases
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Think about what it means to 'get closer' in a mathematical sense.
4Question 4.
Is round-off error significant in computational problems?
- True
- False
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Consider how rounding works in calculations.
Question 5.
Given the PDE 1 - 2phi_xx + phi_yy = 0, classify the equation. Identify A, B, and C, calculate the discriminant, and determine its characteristics.
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Use the discriminant method to classify equations.
Question 6.
Apply Von Neumann stability analysis on the equation u_t = a*u_xx. Derive the condition for stability in terms of the grid spacing and time step.
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Think about how to isolate alpha in the equation governing stability.

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