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Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…

Computational Physics · Physics 2024-01-12 Ce Guan , Jianyu Zhang , Zhen Li , Yongbo Deng

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime ($Re = 0.01$). The problem is numerically solved with the finite-volume method assuming axial symmetry, absence…

Fluid Dynamics · Physics 2021-04-14 F. Pimenta , M. A. Alves

We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…

Numerical Analysis · Mathematics 2025-04-16 Edmund Bell-Navas , David Portillo , Ignacio Romero

We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be…

Fluid Dynamics · Physics 2007-05-23 Laurits H. Olesen , Fridolin Okkels , Henrik Bruus

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou

Heat exchangers incorporating triply periodic minimal surface (TPMS) lattice structures have attracted considerable research interest because they promote uniform flow distribution, disrupt boundary layers, and improve convective…

Computational Physics · Physics 2025-12-12 Kazutaka Yanagihara , Jun Iwasaki , Kiyoto Saso , Taichi Yamashita , Shomu Murakoshi , Akihiro Takezawa

We investigate multi-physical topology optimization for microfluidic mixers employing the phase-field model. The optimization problem is formulated using a modified Ginzburg-Landau free energy functional. To eliminate fluid blockage in…

Optimization and Control · Mathematics 2025-10-23 Zongyuan Liu , Jiajie Li , Shengfeng Zhu

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer (Nu) between and hot and cold walls, for a given rate of viscous dissipation by the flow (Pe$^2$). In the case of no flow, we show…

Fluid Dynamics · Physics 2023-09-29 Silas Alben

T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…

Numerical Analysis · Mathematics 2022-04-14 Ioannis P. A. Papadopoulos , Endre Süli

This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…

Analysis of PDEs · Mathematics 2021-10-28 Diana Rubio , Domingo A. Tarzia , Guillermo F. Umbricht

The demand for high-performance heat sinks has significantly increased with advancements in computing power and the miniaturization of electronic devices. Among the promising solutions, nanofluids have attracted considerable attention due…

Optimization and Control · Mathematics 2025-01-29 Chih-Hsiang Chen , Kentaro Yaji

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…

Optimization and Control · Mathematics 2014-05-15 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle

This article presents a detailed introduction to density-based topology optimisation of fluid flow problems. The goal is to allow new students and researchers to quickly get started in the research area and to skip many of the initial…

Computational Engineering, Finance, and Science · Computer Science 2023-02-03 Joe Alexandersen

As modern electronic devices are increasingly miniaturized and integrated, their performance relies more heavily on effective thermal management. Two-phase cooling methods enhanced by porous surfaces, which capitalize on thin-film…

Machine Learning · Computer Science 2023-10-31 Jonathan Tammer Eweis-LaBolle , Chuanning Zhao , Yoonjin Won , Ramin Bostanabad

We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…

Fluid Dynamics · Physics 2019-10-23 X. Liu , Z. Xie , S. Dong

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar…

Optimization and Control · Mathematics 2024-01-18 Leon Baeck , Sebastian Blauth , Christian Leithäuser , René Pinnau , Kevin Sturm

Triply Periodic Minimal Surface (TPMS) structures are attracting growing attention as promising geometries for next-generation high-performance heat exchangers (HXs), due to their continuous flow paths and high surface-area-to-volume ratio…

Optimization and Control · Mathematics 2025-10-14 Kaito Ohtani , Hiroki Kawabe , Kentaro Yaji , Kikuo Fujita , Vikrant Aute

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to…

Fluid Dynamics · Physics 2026-03-11 Rahul Bhattacharjee , Henning Struchtrup , Anirudh Singh Rana

In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid…

Analysis of PDEs · Mathematics 2021-12-08 Markus Gahn , Maria Neuss-Radu , Willi Jäger

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid…

Optimization and Control · Mathematics 2025-10-14 Leon Baeck , Sebastian Blauth , Christian Leithäuser , René Pinnau , Kevin Sturm