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   Solver for steady or transient fluid flow and solid heat conduction, with
   conjugate heat transfer between regions, buoyancy effects, turbulence,
   reactions and radiation modelling.

1 Equations

For each region defined as fluid, the according equation for the fluid is solved and the same is done for each solid region. The regions are coupled by a thermal boundary condition.

1.1 Equations Fluid

For each fluid region the compressible Navier Stokes equation are solved.

1.1.1 Mass conservation

The variable-density continuity equation is

\frac{\partial \rho}{\partial t} +   \frac{\partial {\rho u}_j}{\partial x_j} = 0

The source code can be found in src/finiteVolume/cfdTools/compressible/rhoEqn.H:

    fvScalarMatrix rhoEqn
      + fvc::div(phi)

1.1.2 Momentum conservation

    \frac{ \partial (\rho {u}_i)}{\partial t} + \frac{\partial}{\partial x_j} \left( \rho {u}_j u_i \right) = 

   - \frac{\partial p_{rgh}} {\partial{x_i}} + \frac{\partial \rho g_j x_j}{\partial x_i}  + \frac{\partial}{\partial x_j} \left( \tau_{ij} + \tau_{t_{ij}} \right)

 u represent the velocity,  g_i the gravitational acceleration,  p_{rgh} = p - \rho g_j x_j the pressure minus the hydrostatic pressure and  \tau_{ij}  and  \tau_{t_{ij}}  are the viscose and turbulent stresses.

1.1.3 Energy conservation

1.2 Equations Solid

2 Source Code