Difference between revisions of "ScalarTransportFoam"

Revision as of 05:04, 17 February 2010

1 Introduction and applications

The scalarTransportFoam is a basic solver which resolves a transport equation for a passive scalar, using a user-specified stationary velocity field.

Typical applications are:

Solution of a scalar convection-diffusion problem on a given velocity field.

2 scalarTransportFoam features, capabilities and limitations

3 scalarTransportFoam capabilities

The scalarTransportFoam solver implements and solves a convection-diffusion scalar transport equation without source terms.

The main features of the solver are:

Solution of a convection-diffusion equation with user-specified boundary conditions
Arbitrary velocity field provided by the user and read at runtime

4 scalarTransportFoam limitations

The main limitations of the solver are:

The diffusion coefficient is assumed to be a constant scalar
An option to solve for the flow coupled with the scalar transport is not available

5 scalarTransportFoam theory

The scalarTransportFoam solver uses a complete convection-diffusion equation, in the incompressible form (the equation is divided by the density)

$\frac{\partial{T}}{\partial t} + \nabla \cdot \left( \mathbf{U} T \right) - \nabla^2 \left( \mathcal{D}_{\textrm{T}} T \right) = 0,$

where $T$ is the transported scalar, $\mathbf{U}$ is the fluid velocity, and $\mathcal{D}_{\textrm{T}}$ is the diffusion coefficient divided by the fluid density, both supposed to be constant.

@@ Line 1: / Line 1: @@
-This application solves the complete unsteady transport equation (convective + diffusive) for a passive scalar in an incompressible fluid:
+== Introduction and applications ==
+The scalarTransportFoam is a basic solver which resolves a transport equation for a passive scalar, using a user-specified stationary velocity field.
+Typical applications are:
+* Solution of a scalar convection-diffusion problem on a given velocity field.
+== scalarTransportFoam features, capabilities and limitations ==
+== scalarTransportFoam capabilities ==
+The scalarTransportFoam solver implements and solves a convection-diffusion scalar transport equation without source terms.
+The main features of the solver are:
+* Solution of a convection-diffusion equation with user-specified boundary conditions
+* Arbitrary velocity field provided by the user and read at runtime
+== scalarTransportFoam limitations ==
+The main limitations of the solver are:
+* The diffusion coefficient is assumed to be a constant scalar
+* An option to solve for the flow coupled with the scalar transport is not available
+== scalarTransportFoam theory ==
+The scalarTransportFoam solver uses a complete convection-diffusion equation, in the incompressible form (the equation is divided by the density)
+<math>\frac{\partial{T}}{\partial t} + \nabla \cdot \left( \mathbf{U} T \right) - \nabla^2 \left( \mathcal{D}_{\textrm{T}} T \right) = 0,</math>
+where <math>T</math> is the transported scalar, <math>\mathbf{U}</math> is the fluid velocity, and <math>\mathcal{D}_{\textrm{T}}</math> is the diffusion coefficient divided by the fluid density, both supposed to be constant.
-<math>
-\frac{\partial T}{\partial t} + \nabla \cdot \left(\varphi T\right) - \nabla^2 \left( D_T \cdot T \right) = 0
-</math>
-where <math>\varphi = U</math> and <math>D_T</math> is a constant.
 [[Category:Basic CFD solvers]]