Implicit-adjoint finite-volume topology optimization of two-dimensional conjugate heat transfer

[2608.19426] Implicit-adjoint finite-volume topology optimization of two-dimensional conjugate heat transfer Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2608.19426 (math) This paper has been withdrawn by Sam Yang [Submitted on 19 Aug 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Implicit-adjoint finite-volume topology optimization of two-dimensional conjugate heat transfer Authors: Sam Yang No PDF available, click to view other formats Abstract: Designing compact, high-efficiency thermal architectures requires resolving the competing demands of solid conduction, fluid convection, and flow resistance within highly constrained physical envelopes. Density-based topology optimization provides a systematic framework for synthesizing these coupled layouts, yet the reproducibility and numerical stability of the resulting designs depend critically on the underlying discrete solvers and adjoint sensitivity mechanics. In this work, we present a transparent, self-contained two-dimensional finite-volume formulation on a staggered Marker-and-Cell grid for conjugate heat transfer governed by design-dependent energy transport coupled to Stokes--Brinkman or Darcy flow at fixed solid volume. To prevent spurious artificial thermal sources in porous, weakly compressible Brinkman domains, the discrete advection operator is constructed to satisfy the identity $\mathbf{u}\cdot\nabla T=\nabla\cdot(\mathbf{u}T)-T(\nabla\cdot\mathbf{u})$ cellwise, ensuring that uniform temperature fields remain exact discrete nullspaces even under inexact continuity satisfaction. Reverse-mode derivatives are evaluated via the implicit function theorem rather than unrolled iterative loops, yielding exact discrete adjoints with bounded memory requirements. The discrete operators are systematically validated through the method of manufactured solutions and directional Taylor remainder tests. Four representative thermofluid design benchmarks are optimized using a projected-gradient scheme with $\beta$-continuation, wherein candidate iterates are accepted and published only upon satisfying rigorous, predeclared gates on residual convergence, mass conservation, volume feasibility, and numerical finiteness. The resulting formulation provides an inspectable, deterministic reference stack for verifiable conjugate thermofluidic topology optimization. Comments: the paper is not novel enough; need further investigation Subjects: Numerical Analysis (math.NA) Cite as: arXiv:2608.19426 [math.NA] (or arXiv:2608.19426v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.19426 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sam Yang [ view email ] [v1] Wed, 19 Aug 2026 20:25:18 UTC (330 KB) [v2] Thu, 27 Aug 2026 01:47:31 UTC (1 KB) (withdrawn) Full-text links: Access Paper: Withdrawn Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Implicit-adjoint finite-volume topology optimization of two-dimensional conjugate heat transfer#677751
• Heating of a semi-infinite Hooke chain#677358
• Heating of a semi-infinite Hooke chain#674161
• Restoring heat and particle flow in strongly coupled non-equilibrium devices#659291
• Restoring heat and particle flow in strongly coupled non-equilibrium devices#657155