3D Transient Fluid Flow

Simulate the flow through a technical object with the Navier–Stokes equation:

Here is the vector-valued velocity field in three dimensions, is the pressure and the identity matrix. and are the density and viscosity, respectively.

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Load the finite element package to generate a mesh.

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Out[2]=2

Visualize the mesh.

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Specify the transient viscous Navier–Stokes equation with viscosity and density .

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Specify a function that ramps up the inflow velocity.

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Specify an inflow profile.

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Specify an inflow boundary condition on the top.

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Specify an outflow boundary condition on the right.

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Specify no-slip boundary conditions on the remaining walls.

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Group the boundary conditions.

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Set up initial conditions such that the system is at rest.

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Time-integrate the Navier–Stokes equation on a mesh with specified spacing while interpolating the velocities with second order and the pressure with first order.

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Out[12]=12

Inspect the amount of memory used in gigabytes.

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Out[13]=13

Compute the range of the pressure distribution.

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Out[14]=14

Visualize the pressure distribution.

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Out[15]=15

Compute the range of the velocity distribution.

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Visualize the total velocity and a vector field of the velocity.

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Out[17]=17