Question 2 Why does the grid need to be refined more on the downstream side than on the upstream side of the obstacle when the flow is laminar or turbulent?

The need to refine the grid more on the downstream side than on the upstream side of an obstacle when the flow is laminar or turbulent is primarily due to the complexity of the flow patterns that occur after the fluid has interacted with the obstacle.

1. Flow Characteristics: In both laminar and turbulent flows, the fluid's behavior changes significantly after it encounters an obstacle. Upstream, the flow can be relatively uniform, but downstream, it becomes more complex due to separation, reattachment, recirculation, and wake formation.

2. Capturing Details: To accurately capture these phenomena in numerical simulations, a finer grid is required. A finer grid allows for a more detailed representation of the flow field, which in turn leads to more accurate results.

3. Turbulence Modeling: In the case of turbulent flows, the range of turbulent scales can be quite large in the wake of the obstacle. To accurately resolve these scales, a refined grid is necessary.

4. Accuracy: The downstream side of the obstacle is where most of the action happens in terms of flow physics. Therefore, having a refined grid on the downstream side ensures that the simulation is accurate where it matters most.

In conclusion, refining the grid on the downstream side of an obstacle is crucial for accurately capturing the complex flow phenomena that occur in both laminar and turbulent flows.