A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches

Li，Futuan1; Yang，Jiang1,2,3

2022-08-01

10.1016/j.cma.2022.115195

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING   Impact Factor & Quartile

0045-7825

1879-2138

In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the fluids and the Ginzburg-Landau energy functional as a regularizing term for the generated diffusive interface, together with a Lagrangian multiplier for volume constraint. An efficient decoupled scheme is proposed to implement by the gradient flow approach to decrease the objective function. In each loop, we first update the velocity field by solving the Stokes equation with the phase field variable given in the previous iteration, which is followed by updating the phase field variable by solving an Allen-Cahn-type equation using a stabilized scheme. We then take the cut-off post-processing for the phase-field variable to constrain its value in [0, 1]. In the last step of each loop, the Lagrangian parameter is updated with an appropriate artificial time step. We rigorously prove that the proposed scheme permits an unconditionally monotonic-decreasing property. To enhance the overall efficiency of the algorithm, in each loop we update the phase field variable and Lagrangian parameter several time steps but update the velocity field only one time. Numerical results for various shape optimizations are presented to validate the effectiveness of our numerical scheme. (c) 2022 Elsevier B.V. All rights reserved.

Shape optimization in Stokes-flows Phase-field method Decoupled schemes Energy stability

SCI ; EI

English

First ; Corresponding

National Natural Science Foundation of China (NSFC)[11871264] ; NSFC/Hong Kong RGC Joint Research Scheme[NSFC/RGC 11961160718] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design, China[2019B030301001]

Engineering ; Mathematics ; Mechanics

Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics

WOS:000833549600007

ELSEVIER SCIENCE SA

20222612275796

Iterative methods ; Lagrange multipliers ; Phase transitions ; Velocity

Physical Chemistry:801.4 ; Optimization Techniques:921.5 ; Numerical Methods:921.6

COMPUTER SCIENCE

2-s2.0-85132710519

Web of Science

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518000,China
2.National Center for Applied Mathematics Shenzhen (NCAMS),Shenzhen,518055,China
3.SUSTech International Center for Mathematics & Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China

Li，Futuan,Yang，Jiang. A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2022,398.

Li，Futuan,&Yang，Jiang.(2022).A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,398.

Li，Futuan,et al."A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 398(2022).