Finding Approximate Solutions to the Navier-Stokes Equations Using Automatic Differentiation

Oseen’s equation models the flow past an object by replacing the standard non-linear convection term in the Navier-Stokes equations with the interaction of the velocity field and the velocity of the object itself. Near the body this approximation is only accurate for Re < 1 but by using an effective viscosity proportional to Re^-3/4 the drag could be accurately computed for axisymmetric flow around a wide range of ellipsoidal bodies up to Re ~100. We seek to extend these results to higher Re and different flows past objects by utilising the power of automatic differentiation in jax to optimise over a wide range of linear terms. We hope that this will give a better qualitative understanding of the driving mechanisms of the full equations.