CFD Methodology

As an example implementation, the cost functions (section 2.1) and the dynamically generated boundary conditions (section 2.2) were applied in a CFD optimization routine. First, a simple 2D geometry was parametrized in terms of five design variables: a,  b,  c,  d,  e. Using a Python-script (36) the geometry was generated depending on these design parameters. BlockMesh (OpenFOAM (35)) was used to mesh the geometry. The Eulerian-Eulerian solver twoPhaseEulerFoam (OpenFOAM) was used to simulate the drug release through the device for high and low flow-rate boundary conditions. Transient boundary conditions were applied using the OpenFOAM library swak4Foam (37). A Python-script (36) determined the drug-release profiles as a function of the scaled inhaled volume x for each boundary condition and then calculated the cost functions C_A and C_B.

A total cost function C_tot = w_AC_A + w_BC_B was calculated (where w_A and w_B are weightings). The cost function C_tot was minimized by systematically changing the geometry using a steepest gradient-descent method, see e.g. (38).