[aliabdullahnust]

I have to model turbulence using MiLES. I have just started and few questions. I hope somebody can answer them.

MiLES uses a high-resolution numerical scheme to solve to un-filtered Navier stokes Equation, right?

1. What is the difference between a High-Resolution numerical Scheme and Higher Order numerical scheme, are they the same?

2. We do conventional LES to reduce the mesh resolution by modeling the sub-grid scale eddies. As an alternate approach, how does MiLES reduce the mesh requirement? Can we say that the use of high-resolution scheme in MiLES allows us to use a coarser grid? So can we say that High-resolution provides an accurate solution for an even coarser grid?

[LuckyTran]

1. They refer to different properties of schemes. Strictly speaking, higher order refers to the rate of truncation error with respect to the grid size and high resolution refers to the resolving power for a given grid size (i.e. how well does this scheme reproduce a sharp gradient or a shock). Of course high resolution schemes will naturally also be high order schemes so they come hand-in-hand. To avoid ambiguity, it's best to simply state what is the scheme in question, unless you are specifically analyzing the truncation error or the resolving power. Most people don't need to know such details.



2. In conventional filtered LES, kinetic energy gets transferred from the filtered/resolved scales to the subgrid scales by the subgrid model. In MILES, there is no subgrid scale model, the discretization schemes and their own natural dissipation removes the energy from the resolved scales. Both methods allow you to use coarse grids compared to DNS since you do not need mesh resolution requiring you to resolve all the way down to the Kolmogorov scales. It depends on how good is your subgrid model and how good is your MILES scheme whether conventional LES can be done with a coarse/finer grid than MILES, no universal truth here until you name a specific implementation.

[FMDenaro]

Originally Posted by aliabdullahnust

I have to model turbulence using MiLES. I have just started and few questions. I hope somebody can answer them.

MiLES uses a high-resolution numerical scheme to solve to un-filtered Navier stokes Equation, right?

1. What is the difference between a High-Resolution numerical Scheme and Higher Order numerical scheme, are they the same?

2. We do conventional LES to reduce the mesh resolution by modeling the sub-grid scale eddies. As an alternate approach, how does MiLES reduce the mesh requirement? Can we say that the use of high-resolution scheme in MiLES allows us to use a coarser grid? So can we say that High-resolution provides an accurate solution for an even coarser grid?

No, using MILES the numerical solution is supposed to be that of the implicitly filtered NSE. The SGS term is not explicitly added but is supposed that the monotone scheme mimics the effects of the turbulence model.


High resolution schemes must be analysed in spectral space, you will see they tend to approach the spectral resolution but are never able to resolve components at frequencies higher than the Nyquist one. This is the implicit filtering induced by the grid resolution. You increases the accuracy only of the resolved components.