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boundaryField

boundaryField
{
    movingWall      
    {
        type            zeroGradient;
    }

    fixedWalls      
    {
        type            zeroGradient;
    }

    frontAndBack    
    {
        type            empty;
    }
}

// ************************************************************************* //

boundaryField defines boundary conditions for each mesh boundaries parameter type defines the name of the boundary condition e.g. boundary condition zeroGradient is so called homogeneous Neumann boundary condition, which means that quantity gradient is zero in direction perpendicular to the boundary e.g. boundary condition empty means, that there is no flow considered in the direction perpendicular to the boundary

Let us take a look at the velocity file :
# cat $FOAM_RUN /cavity/0/U

 

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  dev                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0 0 0);

boundaryField
{
    movingWall      
    {
        type            fixedValue;
        value           uniform (1 0 0);
    }

    fixedWalls      
    {
        type            noSlip;
    }

    frontAndBack    
    {
        type            empty;
    }
}

// ************************************************************************* //

Velocity U is a vector and has three components (Ux, Uy, Uz) At the wall, a fixed value is usually prescribed for velocity (Dirichlet boundary condition): fixedValue, which needs its value, either uniform or nonuniform Condition uniform (0 0 0) means the velocity is zero at the wall or you can use an equivalent boundary condition: noSlip. Condition uniform (1 0 0) means the velocity is 1 m/s in direction with respect to coordinate x (wall is moving)

Compressible Mathematical Model

The computational model solves following system of equations:

1 3
3 3
2 3
3 3
5 3
6 2
7 1
8 2
  • Mass conservation [*]
  • Momentum conservation [*]
  • Energy conservation [*] and [*], two options
  • where: Einstein summation is used, $ \color{white} \partial$ is partial derivative, $ \color{white} x_i$ is i-th Cartesian coordinate, $ \color{white} \rho$ is density, $ \color{white} u_i$ is i-th velocity vector component, $ \color{white} t$ is time, $ \color{white} p$ is static pressure, $ \color{white} \tau$ shear stress tensor, $ \color{white} \delta_{ij}$ is Kronecker delta, $ \color{white} e_0$ is total specific energy, $ \color{white} \mu$ is dynamic viscosity, $ \color{white} S_{ij}$ is rate-of-deformation tensor, $ \color{white} T$ is static temperature, $ \color{white} Pr$ is Prandtl number, $ \color{white} R$ specific gas constant, $ \color{white} C_p$ specific heat capacity (at constant pressure), $ \color{white} C_v$ specific heat capacity (at constant volume), $ \color{white} q_i$ i-th heat flux component (Fourier law), $ \color{white} \lambda$ heat conductivity coefficient.
  • The whole system is closed with boundary conditions.