Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow

We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too small to make fully resolved direct numerical simulations feasible. Unfitted finite element methods with ghost-penalty stabilisation are well suited to fluid-structure-interaction problems as posed by this setting, due to the flexible and accurate geometry handling and for allowing topology changes in the geometry. In the computationally under resolved setting posed here, accurate computations of the forces by their boundary integral formulation are not viable. Furthermore, analytical laws are not available due to the shape of the particles. However, accurate values of the forces are essential for realistic motion of the particles. To obtain these forces accurately, we train an artificial deep neural network using data from prototypical resolved simulations. This network is then able to predict the force values based on information which can be obtained accurately in an under-resolved setting. As a result, we obtain forces on very coarse and under-resolved meshes which are on average an order of magnitude more accurate compared to the direct boundary-integral computation from the Navier-Stokes solution, leading to solid motion comparable to that obtained on highly resolved meshes that would substantially increase the simulation costs.