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Electrostatic equation

Flux equation

FEM

Description

This equation calculates viscous fluid flows using the Navier-Stokes equations.

For info about the math of the equation, see the Elmer models manual, section Navier-Stokes Equations.

Usage

1. Add an Elmer solver.
2. Select it in the Tree view.
3. There are several ways to invoke the command:
   • Press the Flow equation button.
   • Select the Solve → Flow equation option from the menu.
4. Change the equation's solver settings or the general solver settings if necessary.

Solver Settings

For the general solver settings, see the Elmer solver settings.

The flow equation provides these special settings:

• ДанныеDiv Discretization: To be set to true for incompressible flow for more stable discretization when the Reynolds number increases.
• ДанныеFlow Model: The flow model that should be used. The default Full includes convection and time derivative terms in the model. No convection switches off the convection terms and the Stokes model switches off the convection terms and the (explicit) time derivative terms.
• ДанныеGradp Discretization: If set to true pressure Dirichlet boundary conditions can be used. Also the mass flux is available as a natural boundary condition.
• ДанныеVariable: Optional only for calculations in 2D: You can change the default of 3 to 2.
  Note: In this case none of the flow velocity boundary conditions can have a specified z-component.

Equation:

• ДанныеConvection: The type of convection to be used in the Heat equation.
  Note: For thermal flows it must be set to Computed (the default).
• ДанныеMagnetic Induction: If set to true the magnetic induction equation will be solved along with the Navier-Stokes equations.

Notes for Convergence

If the solver results do not converge, you can try these things (in the given order):

1. Reduce the ДанныеRelaxation Factor, see the nonlinear system settings.
2. Increase the value for ДанныеNonlinear Newton After Iterations, see the nonlinear system settings.
3. Reduce the number of CPU cores used, see the FEM preferences.
4. Increase the mesh density (make it more fine).

Analysis Feature Information

The flow equation takes the following analysis features into account if they are set:

• Flow velocity boundary condition
• Initial flow velocity condition
• Pressure load
• Initial pressure condition (introduced in 0.21)

Notes

• Except for calculations in 2D, for all above boundary conditions it is important that they act on a face or body. Boundary conditions for 3D set to lines or vertices are not recognized by the Elmer solver.
• Since Pressure load can only be set to faces, pressure loads cannot be used for calculations in 2D.
• If there is no Pressure load set, Initial pressure condition will only be taken into account if ДанныеGradp Discretization is set to true.

Results

The results are the velocity in ${\displaystyle {\rm {m/s}}}$ and the pressure in ${\displaystyle {\rm {Pa}}}$. If there is no Initial pressure condition and Pressure load given, the resulting pressure will be relative not absolute. Since pressure must act on a face, absolute pressure results cannot be obtained in 2D simulations.

Electrostatic equation

Flux equation

FEM