Adjoint data assimilation for a two-fluids flow with deformable interface

The aim of data assimilation is to recover more kinematics and dynamics details from observations by combing numerical model and measurement. In this study, we have developed an adjoint data assimilation model for assimilating measurements in two-fluids flow simulation with deformable interfaces. The coupled level-set and volume-of-fluid (CLSVOF) method is used to capture the liquid-gas interface in the simulation. An adjoint solver for the Navier-Stokes equations with the CLSVOF method is developed. In this method, a cost function is defined for the error between simulation and measurement. The cost function is reduced in an optimization process with the gradient information provided by the adjoint solver. Our model is validated by matching the gradients calculated by the adjoint solver with the approximated gradients by the finite difference method. Canonical problems of surface waves and vortices interacting with a free surface are considered as test cases. It is found that the flow structure and interface geometry can be successfully reconstructed by incorporating velocity measurements at several positions into the data assimilation model.