Preserving solid-body mass properties with surface-only discretization in ConstraintIB

[liwei yao]

Dear IBAMR developers,

I am currently using the ConstraintIB framework to simulate a three-dimensional self-propelled fish undergoing rigid-body motion.

In my present implementation, the fish body is discretized using a volumetric Lagrangian representation, i.e., the interior is fully filled with Lagrangian points. However, in 3D this approach leads to substantial memory consumption.

To reduce memory usage, I modified the discretization to a surface-only (hollow shell) representation, so that interior Lagrangian points are no longer generated. This significantly decreases the runtime memory footprint.

However, after switching to the hollow representation, the total mass and the center-of-mass location both change.

It appears that in ConstraintIB, the rigid-body mass properties depend on the Lagrangian discretization and the specified solid density parameter (e.g., rho_solid = RHO). Therefore, I would like to ask:

Without modifying the IBAMR core source code, is it possible—by changing only the kinematics class or the example.cpp—to achieve the following?

Although the fish is geometrically represented as a hollow shell, can it dynamically behave as a solid body with the original mass and center-of-mass properties corresponding to the fully filled (volumetric) discretization?

My goal is to reduce memory usage while preserving physically consistent rigid-body dynamics.

Thank you very much for your time.

Best regards,

Li-Wei

[Boyce Griffith]

ConstraintIB is setup so that the structure has a volumetric representation. Unless you want to impose the motion of the fluid-structure interface, correctly handling the case in which you only have coupling between the fluid and the structure requires a different coupling approach. One way to do this is detailed in this paper:

This work uses the IIM implementation provided in IBAMR to reconstruct the exterior fluid tractions that are acting on the fluid-solid interface, and uses those as forcing terms for a stand-alone rigid body dynamics solver. A limitation of the approach is that it uses a penalty formulation that, at the present time, usually requires small time step sizes. My guess is that total runtime will be lower using ConstraintIB with a volumetric model.

In principle, you should be able to reconstruct exterior fluid tractions when using regularized delta functions through extrapolation. However, with what is currently implemented in IBAMR, I think that this will require a spatial resolution that is fine enough so that the support of the regularized delta function is relatively small compared to the size of the boundary layer. (In fact, I think that there are ways to avoid this, but we are still working out the details and don’t have anything that is ready for general use.)

Anyway, I think that my recommendation would be to stick with a volumetric representation if you are satisfied with the simulation results. Also, if you haven’t upgraded IBAMR recently, more recent versions should be faster and have a smaller memory footprint.

— Boyce

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