I have never seen that a FVM is used in a direct numerical simulation. Only spectral and FD methods are widely used. What could be the reason for this? Can FVM make an effective and accurate DNS solver?
FVM is less accurate than FDM. It can be of 1st or 2nd order accurate. Also, calculating cell centred value only will not give accurate result when length scale is very small.
Finite Volume Methods, unlike FD methods ensure the conservation of physical quantities like mass, momentum and energy in discrete sense too.
This means that the discretized form of integral form of Navier-Stokes equations, will allows variations of flow properties only through fluxes across the boundaries of the control volumes. No numerical sources or sinks will be present in the numerical solution, provided the right stability constraints on the space/time integration procedure.
Such point is of fundamental importance in the numerical simulation of turbulence through DNS where all the turbulent scales have to be resolved by the simulation.
Numerical discretization does not have to infer both energy transfer mechanism, which occurs without net dissipation, or dissipative mechanisms at the level of Kolmogorov scale.
High Order (Fourth) order Finite Volume methods applied to DNS will do the rigth job though being computationally more expensive.
Best Regards,
Andrea
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