Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
This work addresses a computational bottleneck in fluid dynamics for researchers modeling inertial particle motion, offering an incremental improvement by enabling more accurate simulations without neglecting the Basset force.
The paper tackles the challenge of numerically solving the Maxey-Riley-Gatignol equations, which include the complex Basset force integral term, by approximating this history term using neural networks within a universal differential equations framework, resulting in a system of ordinary differential equations solvable with standard methods like Runge-Kutta.
The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods.