A differentiable solver for incompressible flows

In many biological and environmental flow problems, there is need to perform inverse calculation to determine model parameters. While traditional Computational Fluid Dynamics (CFD) approaches were successful in solving the forward problem, the large variation of model parameters in inverse problems prohibits the use of traditional CFD methods in these cases. We present a differentiable solver for simulating incompressible flows based on hybrid staggered/non-staggered approach using JAX library to carry out inverse calculation. Using a structured grid, the fluxes are stored at cell faces while the pressure fields are at volume centers. The fractional step method is applied to solve the incompressible Navier-Stokes equations. The momentum equation is solved using the Runge-Kutta 4^th order method. The Poisson equation is solved using the Numpy library. In the forward problem, our solver is validated through two standard 2D problems: (i) lid-driven cavity flow; and (ii) Taylor-Green vortex. In the inverse problems, our differentiable solver is used to determine model’s parameters (viscosity) given sparse data from limited numbers of sensors.