1.3.1 Single Phase Flow

For an arbitrary scalar $\phi_k$, ANSYS FLUENT solves the equation

where $\Gamma_{k}$ and $S_{\phi_k}$ are the diffusion coefficient and source term supplied by you for each of the $N$ scalar equations. Note that $\Gamma_{k}$is defined as a tensor in the case of anisotropic diffusivity. The diffusion term is thus $\nabla \cdot \left({\bf\Gamma_k} \cdot \phi_k \right)$

For isotropic diffusivity, $\Gamma_k$ could be written as $\Gamma_k I$ where I is the identity matrix.

For the steady-state case, ANSYS FLUENT will solve one of the three following equations, depending on the method used to compute the convective flux :

• If convective flux is not to be computed, ANSYS FLUENT will solve the equation

  
  

  
  

  where ${\Gamma}_k$ and $S_{\phi_k}$ are the diffusion coefficient and source term supplied by you for each of the $N$ scalar equations.

• If convective flux is to be computed with mass flow rate , ANSYS FLUENT will solve the equation

  
  

  
  

• It is also possible to specify a user-defined function to be used in the computation of convective flux. In this case, the user-defined mass flux is assumed to be of the form

  
  

  
  
  where $d \vec{S}$ is the face vector area.