# GfsSourceViscosity

### From Gerris

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- | GfsSourceViscosity solves the diffusion equation for the velocity (a vector quantity obviously) while [[GfsSourceDiffusion]] solves the diffusion equation for a scalar quantity. In the case of a spatially uniform viscosity the two are strictly equivalent since — in the case of an incompressible fluid — the vector diffusion equation for the velocity can be split in independent scalar diffusion equations for each of the Cartesian components of the velocities. | + | [[GfsSourceDiffusion]] solves the diffusion equation for a scalar quantity, while '''GfsSourceViscosity''' solves the diffusion equation for the velocity (a vector quantity obviously). In the case of a spatially uniform viscosity the two are strictly equivalent since—in the case of an incompressible fluid—the vector diffusion equation for the velocity can be split in independent scalar diffusion equations for each of the Cartesian components of the velocities. |

To sum up, using GfsSourceViscosity is safe in all cases, regardless of whether the viscosity is uniform. | To sum up, using GfsSourceViscosity is safe in all cases, regardless of whether the viscosity is uniform. | ||

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- | In the case where the density (specified using [[GfsPhysicalParams]]) is not unity, the diffusion coefficient is the [[w:Viscosity#Viscosity_coefficients|dynamic viscosity coefficient]]. | ||

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- | The syntax in parameter files is: | ||

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- | [ [[GfsSourceVelocity]] ] [ [[GfsDiffusion]] ] | ||

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- | where <code>[[GfsDiffusion]]</code> defines the dynamic viscosity of the fluid. | ||

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- | <examples/> |

## Revision as of 11:33, 20 October 2012

GfsSourceDiffusion solves the diffusion equation for a scalar quantity, while **GfsSourceViscosity** solves the diffusion equation for the velocity (a vector quantity obviously). In the case of a spatially uniform viscosity the two are strictly equivalent since—in the case of an incompressible fluid—the vector diffusion equation for the velocity can be split in independent scalar diffusion equations for each of the Cartesian components of the velocities.

To sum up, using GfsSourceViscosity is safe in all cases, regardless of whether the viscosity is uniform.