Dear All, I am a student starting to work on CFD. Would any please share thoughts on SOURCE TERMS in NS equations. What is the meaning of source/sink terms. Why these terms are required at all. Warm regards, Sas

The NS equations (and, more generally, transport equations) include transient, convection and diffusion terms. Any other terms, which do not fit into these, are classified as "source/sink" terms. For example, in the momentum equations, gravity acts as a momentum source term, and in the energy equation, externally-applied heat is an energy source term.

you can distinguish four terms in every conservation law like mass, energy,momentume and ... . three of them are well known and easy to distinguish. these are diffusion term, advection term and time term. All the other terms are put in the source(sink) term.In NS equation the gravity force term and pressure gradiant are sink term.

Thank for the response. But My question was not to distinguish these terms but I wanted to know the meaning and significance of there terms. What would happen if there is no source or sink terms in NS equations. Why these terms are required at all. In case anyone has any idea regarding these questions, please respond. Warm regards, Sas

Hi, Sas.

Source terms may be used in many ways. Consider the following 3.

1. Sometimes the physical problem in question involves a body force, like gravity. Then it needs to be reflected in the mathematical formulation, hence there should be a corresponding term in the equation. In general, this term cannot be written in a special form characteristic for conservation laws (mathematically speaking, it cannot be represented as a divergence). It is a custom among mathematicians to call such terms "source terms". In other words, we include these terms because the physics of the problem requires them, and then we call them source terms because this is what they are.

2. Source term can be used for approximate description of under-resolved geometries. For example, instead of gridding a vortex generator in all the details, it is possible just to add a body force (= source term) which will produce a vortex similar to the vortex produced by the vortex generator.

3. Source term can be used for checking the correctness of the code. Codes can be tested against exact solutions but exact solutions are rare and usually they are not sufficiently challenging: what makes the problem solvable analyticly also makes it easier to solve numerically. If the code allows prescribing an arbitrary source term, one can take an arbitrary expression for the velocity (satisfying continuity, of course) and pressure, substitute it into the Navier-Stokes equations with a source term and calculate the corresponding source term. This can be done on paper or using a computerised algebra system like Maple or Mathematica. One then substitutes this source term into the code, solve the equations numerically, and compares the numerical solution with expressions for the velocity and pressure. This is a very powerful test indeed.

Hope this helps.

Sergei

Thank you very much for explaining that in such a nice way... Sas