[MITgcm-support] Inviscid fluid modeling

[Martin Losch]

Hi Pavel (?),

by default, the MITgcm code solves the Reynolds-averaged hydrostatic, Boussinesq Navier-Stokes equations on the sphere, additional assumptions make this the so-called Primitive Equations (PE). There are flags that can turn on different parameterisations of the turbulent eddy viscosity, and/or non-hydrostatic dynamics. You can also interpret the equations as pure Navier-Stokes with molecular viscosity. On a cartesian grid some of the PE assumptions are not necessary (e.g. thin-shell approximation) and you can use the code for LES or DNS type Navier-Stokes simulations.

As far as I understand the viscosities are also required for numerical stability reasons. Therefore, from a numerical points of view you’ll need a different numerical scheme to solve the inviscid Euler equations. This scheme needs to be unconditionally stable (which will involve some implicit viscosity). In the same way, reducing the explicit viscosities towards zero will recover the Euler equations, but at the cost of numerical instability.

I am not sure what you mean by changing the boundary conditions. An inviscid boundary conditions (free-slip, v.Neuman) would be consistent with vanishing viscosity. The no-slip boundary condition (Dirichlet with tangential velocity =0 on the boundary) parameterizes a viscous boundary layer, but does not require viscosity outside of this boundary layer. Both options are available with the MITgcm code.

Martin

> On 14. Aug 2019, at 09:42, Павел Лобовиков <plobovikov at gmail.com> wrote:
> 
> Hi folks!
> I have one theoretical question regarding the equations underlying MITgcm.
> If we are dealing with the movement of a viscous fluid it's obvious that we are solving the Navier-Stokes equations. 
> But if I want to simulate the motion of an inviscid fluid I have to go back to Euler equations.
> The question is: how is viscosity deactivation implemented in MITgcm?
> 
> I have two assumptions:
> 1. We need to go back to Euler equations and change the boundary conditions.
> 2.  We remain within the framework of the Navier-Stokes equations and just transit to the limit ViscocityCoefficient -> 0
> 
> Thanks!
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