Implementation of an adjoint-based optimization with scalar transport

Paper in proceeding, 2014

A sensitivity analysis of a particle distribution at the outlet of a 2D-channel is presented. A convection-diffusion equation is used to represent the distribution of particles in a flow. The flow is governed by the Reynolds-Averaged Navier-Stokes equations. The particles follow the medium to the outlet, where the goal is to obtain uniform distribution of the particles. A goal function for the particle distribution at the outlet is presented, and the gradient of the goal function with respect to the normal motion of the surface is calculated. The calculation of the gradient is performed by applying the so-called adjoint method. For this, the adjoint scalar transport equation and the relevant adjoint RANS equations are implemented. The calculation cost of the entire sensitivity field is roughly twice the cost of a standard convection-diffusion particle simulation. This results in computationally cheap gradients compared to traditional methods. The results are validated by comparing the gradients calculated using the adjoint method to gradients obtained using numerical differentiation.