Tedori-Callinan Lecture Series: 2016
"Topology Optimization for Thermal-Fluid Problems Using Unstructured Finite Volume Schemes"
Presented by: Jayathi Y. Murthy
Dean, Henry Samueli School of Engineering and Applied Science
University of California, Los Angeles
Tuesday, October 4, 2016
Wu and Chen Auditorium, Levine Hall
Topology optimization is a method for developing optimized geometric designs that maximize a quantity of interest (QoI) subject to constraints. Unlike shape optimization, which optimizes the dimensions of a template shape, topology optimization does not start with a pre-conceived shape. Instead, the algorithm builds the geometry iteratively by placing material pixels in a specified background domain, aiming to maximize the QoI subject to a constraint on the volume of material or other constraints. The power of topology optimization lies in its ability to realize design solutions that are not initially apparent to the engineer. Topology optimization, though well established in structural applications, has not percolated to the thermal-fluids community to any great degree. However, the methodology has immense application potential in the area of fluid flow, heat and mass transfer, particularly with the advent of 3D printing.
In this talk, we describe recent work on topology optimization based on widely-used unstructured finite volume schemes employing co-located sequential pressure-based solvers. In our work, the solid isotropic material with penalization (SIMP) approach is used in conjunction with a gradient-based optimization algorithm. Sensitivity derivatives of the QoI with respect to design variables are computed through a discrete adjoint method. The Method of Moving Asymptotes (MMA) is used for optimization. A hallmark of sequential pressure-based methods schemes is that the complete Jacobian is never assembled, causing difficulties with using gradient-based schemes. An important contribution of the work is the development of an automatic differentiation library, Rapid, to compute accurate Jacobians and other necessary derivatives to address this issue. An essential feature of ℛapid is that it is not necessary to write new code to find sensitivities when new physics, such as turbulence models, are added, or when new cost functions are considered. The methodology is demonstrated on a variety of heat conduction and laminar and turbulent flow and heat transfer problems. The methodologies developed here are very general and are easily translated to use in industry, and for problems with more complex physics and more realistic constraints.
Jayathi Murthy is Dean of the Henry Samueli School of Engineering and Applied Science and Distinguished Professor of Mechanical Engineering at UCLA. She received her Ph.D degree from the University of Minnesota in the area of numerical heat transfer and has worked in both academia and in industry. She served as Director of PRISM: NNSA Center for Prediction of Reliability, Integrity and Survivability of Microsystems at Purdue University. During her employment at Fluent Inc., a leading vendor of CFD software, she developed the unstructured solution-adaptive finite volume methods underlying their flagship software Fluent, and the electronics cooling software package ICEPAK. More recently, her research has addressed sub-micron thermal transport, multiscale multiphysics simulations of MEMS and NEMS and uncertainty quantification in these systems.
She is the recipient of the IBM Faculty Partnership award 2003-2005, numerous best paper awards, the 2009 ASME EPPD Woman Engineer of the Year Award and the 2012 ASME EPPD Clock Award. In 2012, she was named a distinguished alumna of IIT Kanpur, India, and was recently named a recipient of the ASME Heat Transfer Memorial Award. Prof. Murthy serves on the editorial boards of Numerical Heat Transfer and International Journal of Thermal Sciences and is an editor of the 2nd edition of the Handbook of Numerical Heat Transfer. She has served on numerous national committees and panels on electronics thermal management and CFD, and is the author of over 280 technical publications.