Computational Fluid Dynamics "Boundary Condition"

Hello, this is E8IGHT, a software company that develops particle-based CFD Software NFLOW.

The topic we are going to discuss is “Boundary Condition” where it’s always mentioned in the field of computational fluid dynamics.

Boundary condition is a condition near a physically valid boundary for accurate analysis of flow in finite computational domain in CFD.

Various boundary conditions exist but in CFD Dirichlet boundary condition and Neumann boundary condition are used a lot. Other that these two, Periodic boundary condition is also used. In SPH (Smoothed Particle Hydrodynamics) technique, the boundary conditions mentioned above are used. Now, let’s briefly look into the representative boundary conditions one by one!

1. Dirichlet Boundary Condition

Dirichlet Boundary Condition is a boundary condition that specifies a value that the function should perform along the boundary of the domain.

u(x) = a

You can assign a specific value such as a in the boundary of the function. The image below shows when Dirichlet boundary condition is applied and velocity of the flow is given 10 m/s at the boundary.

2. Neumann Boundary Condition

Neumann Boundary Condition is boundary condition where it gives a gradient value of the function at the boundary.

∂u/∂x=a

You can assign a specific value of a function’s gradient as shown above in the formula.

The image below shows when the Neumann boundary condition is applied, and gradient is given 0 at the boundary.

3. Periodic Boundary Condition

Periodic Boundary Condition separates the repeated periodic domains and assumes that particles that have exited the computational domain flows back from the opposite side. In computational fluid dynamics, this is often applied to impose boundary conditions.

For instance, in the case of a fan analysis as shown in the image below, you can designate one wing as an analysis area and proceed the analysis.

So far, we have briefly discussed about the boundary conditions used in computational fluid dynamics. Other than boundary condition, there are so many conditions used in CFDs, including SPH!

We will continue to upload contents related to technologies or researches in near future.

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