CFD:
When the solution algorithm is iterative in nature, and
if the solution converges, then,
Can we, by default,
take it for granted
that the associated fluid flow properties
were CONSERVED
(based on the negligible residual values)?
In a iterative solution, the true solution is not obtained. You accept an approximation error for the calculated variables or properties o f the problem.
Regards
If the governing equations and the boundary condition are represented accurately, certainly the converged solution within an acceptable errors is the final approximation solution. The error of this solution depends on size of mesh.
The answer on your question is yes for both steady and unsteady fluid flow. That because the convergence of the solution implies that your algorithm satisfies both consistency and stability conditions for each iteration step.
Regards
The answer is not. First, while conservative and non-conservative continuous formulations of the NSE are mathematically equivalent if the functions are regular, conservation in discrete sense requires the property of the unicity of the computed flux function.
In other words, you need to start from the conservative form of the NSE and write the discrete counterpart in terms of finite volumes where the flux integrated over a surface between adjacent volumes is unique.
This way, the time derivative of any conserved variable in the volume depends only on the properties of the fluxes prescribed at the boundaries.
Conversely, the non-conservative discrete form does not ensure the conservation of the property, even if you reach the convergence.
It depends on which properties you are referring to.
Properties like density, momentum and total energy are "conservative" properties, i.e., they obey conservation laws in a finite dimensional space ( or volume ). In other words, they obey Reynolds transport theorem. Hence, these will be conserved when the iterative solution converges.
Other properties like temperature and pressure are "non-conservative" in nature, hence won't be conserved.
Hirsh's book has a very good introduction about these topics. You can refer it.
- Badges
- Science topic