An Eulerian Divergence Preserving Approach for Partitioned FSI Simulations on

Cartesian GridsM. Mehl, M. Brenk, I. Muntean,

T. Neckel, T. Weinzierl TU München

Povoking Questions

Should we reinvent the wheel

each time

we change the construction of the car?

Povoking Questions

Can we reduce complexity

without loosing

accuracy, efficiency, and generality?

Computer Science View

not application driven

synergies

numerics hardware

modularity, reusability

frameworks

The Partitioned Approach

server fluid+ interpolation

server structure+ interpolation

job

datajob

data

Clientsurfacecoupling

Cartesian Fluid Grids

Cartesian Fluid Grids

• spatially recursive structure

memory efficiency

efficient parallelisation

embedding

• arbitrary local adaptivity

complex geometries

dynamical adaptivity

Fluid Solver – Eulerian Approach

• marker-and-cell

Fluid Solver – Eulerian Approach

octree depth

time (sec)

nodes

7 0.8 203,905

9 4.9 3,288,225

11 48.2 52,662,337

13 662.8 842,687,105

grid generation

Eulerian Fluid Grid – Example

Coupling – Surface Triangulation

Structure Solver – Any Grid

Time Stepping – Algorithm

• fluid: Navier-Stokes

explicit

Chorin‘s projection

• coupling

weak

recover divergence-free flow field

Time Stepping – Algorithm

Time Stepping – Algorithm FLOW COUPLING STRUCTURE

send geometry

initialisation initialisation

update surface

update grid

Chorin‘s proj.

time step

send forces

update surface

update grid

time step

send velocities

Example Application

Conclusions

• modularity

• recursive structure

• physical correctness

simple, but efficient and applicable