2.5.2.1.1. Finite Difference Method

Try these first

1. 1.

   What does CFD stand for?

   Hint

   Think about the study of fluid flows and simulations.

2. 2.

   Define discretization in your own words.

   Hint

   Consider how we transform a curve into individual points.

3. 3.

   What is the main purpose of the Finite Difference Method?

   • To solve complex equations
   • To approximate derivatives
   • To visualize flow fields

   Hint

   What does it mean to approximate something?

4. 4.

   CFD is primarily used in which field?

   • Engineering
   • Mathematics
   • Arts

   Hint

   Think about where fluids commonly need to be analyzed.

5. 5.

   A natural water stream’s velocity field must be analyzed over a 50m stretch. The stream can be approximated as a 1D flow. Calculate the velocity at 5 points using the finite difference method with a grid spacing of 10m. Assume a uniform flow of 3 m/s.

   Hint

   Consider how velocity remains constant in uniform flow.

6. 6.

   Design a simple grid for a 3D domain of a water tank with dimensions of 5m x 5m x 10m. How would you approximate the velocity at the corners using finite difference values if the velocity at the inflow point is 2 m/s and their neighbors are 1.5 m/s?

   Hint

   Think about how averaging helps smooth out discrepancies.