Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1663–1677 | Cite as

Topology optimization of three-phase interpolation models in Darcy-stokes flow

  • Chao Shen
  • Liang Hou
  • Enlai Zhang
  • Jiahe Lin


This paper extends the topology optimization (TO) methods of fluid flows to design the three-phase (i.e. solid, fluid and porous materials) interpolation scheme. In addition to numerous studies about the optimized layout of regions governed by Darcy-Stokes equations, this paper aims to minimize the pressure attenuation in multiple phase interpolation models. The optimized distribution is obtained by considering both the fluid permeability through the porous media and impenetrable inner walls (solid phase) and neglecting buoyancy and other external body forces. Each material phase is assigned with two design variables that are projected into the element space via the regularized interpolation functions. The solid isotropic material with penalization (SIMP) interpolation functions, which is initially developed for minimizing compliance of multiple structural materials, is applied to TO processes of Darcy–Stokes flow. The fields are divided into the design and non-design domains, and TO layouts are assembled to satisfy the given performance functions. The smoothed Heaviside projection filter and Helmholtz-type Partial Differential Equation (PDE) based filter are utilized to produce discrete solutions in the continuum TO processes. Numerical studies are carried out to verify the proposed interpolation scheme.


Topology optimization Darcy-stokes equation Multiple phase Porous materials 



This work was supported by “Collaborative Innovation Center of High-End Equipment Manufacturing in Fujian”. The authors also would like to thank Professor Gil Hoo Yoon for valuable suggestions during the preparation of the work. In addition, we would like to thank the anonymous reviewers who have helped to improve the paper.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Electrical EngineeringXiamen UniversityXiamenPeople’s Republic of China

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