Accelerating Microfluidic Heat Sink Design: A POD-ROM Approach to Topology Optimization by Dr Athanasios Boutsikakis (Corintis SA)

This talk focuses on accelerating the design of microfluidic heat sinks via topology optimization of the conjugate heat transfer problem. The computational bottleneck of this iterative process is the numerical solution of the Navier-Stokes (NS) equations due to their nonlinearity. The approach presented in this talk leverages the Proper Orthogonal Decomposition (POD) method to develop a Reduced Order Model (ROM) for the NS equations including a Brinkman term. The novelty of this method lies in generating POD snapshots during the topology optimization (online) by capturing solutions of the nonlinear NS equations using a Full Order Model (FOM) based on the Finite Element Method. These snapshots are then used to incrementally generate a singular vector basis, which is subsequently applied via a Galerkin projection to truncate the Taylor expansion of the NS equations within a Newton-Raphson solver. Therefore, during the iterative optimization process, the method alternates between using the FOM for snapshot generation and the creation and solution of the ROM. Using this method for problems of 1-2 million degrees of freedom results in a significant acceleration of the entire topology optimization pipeline by 5-6x. This acceleration is pronounced in the later optimization stages when the geometry evolution is subtle, while the difference between the final designs obtained by the FOM and the ROM is not significant. Thus, this approach enables faster and more efficient optimization of microfluidic heat sink designs, making it a valuable tool for engineers and researchers in the field.