Unit of force in ConstraintIB ForceProjector

[Sagar G Nayak]

Hello all,

In this 2013 paper (https://doi.org/10.1016/j.jcp.2013.04.033) for IBAMR's ConstraintIB module, the unit of forces (both Eulerian and Lagrangian) appear as force densities (N/m^3). However, in the ForceProjector.cpp of falling_sphere problem the unit of force seems to be just Newton.

(https://github.com/IBAMR/IBAMR/blob/6e6c7a46bbccbee51bdb46daf67761076cc5cb2a/examples/ConstraintIB/falling_sphere/ForceProjector.cpp#L150).

Can someone please explain why is it so?
Is this force is changed further in some other files before getting added to NS?

Thanks

[Boyce Griffith]

For models that are based on IBMethod, like ConstraintIBMethod, internally the implementation uses forces on the Lagrangian points instead of force densities. The basic formula looks like:

f_{i,j,k} = sum_l F_l delta_h(x_{i,j,k} - X_l)

Note that delta_h has units of 1/volume, and so this converts a force on the IB points into a force density on the grid.

The reason that IBMethod works like this is to try to facilitate support codimenion-0, 1, and 2 structure models — so the code doesn’t know if the IB force is a force per unit volume, per unit area, or per unit length.

Amneet hopefully will chime in if this is wrong, but I think that for ConstraintIBMethod, models are usually set up so that the volume associated with each IB point is equal to the background grid spacing.

— Boyce

Thanks

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[Amneet Bhalla]

Correct one marker per cell means that volume associated with a marker is h^3 or h^2 in 3d and 2d, respectively.

--Amneet 

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[Sagar G Nayak]

Thank you very much for the answers. It makes sense to me now.

Thanks