Wolfram Language

3D Transient Fluid Flow

Simulate the flow through a technical object with the NavierStokes 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.

Load the finite element package to generate a mesh.

Out[2]=2

Visualize the mesh.

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Out[3]=3

Specify the transient viscous NavierStokes equation with viscosity and density .

Specify a function that ramps up the inflow velocity.

Specify an inflow profile.

Out[6]=6

Specify an inflow boundary condition on the top.

Specify an outflow boundary condition on the right.

Specify no-slip boundary conditions on the remaining walls.

Group the boundary conditions.

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

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

Out[12]=12

Inspect the amount of memory used in gigabytes.

Out[13]=13

Compute the range of the pressure distribution.

Out[14]=14

Visualize the pressure distribution.

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Out[15]=15

Compute the range of the velocity distribution.

Out[16]=16

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

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Out[17]=17

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