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Shape Optimization of Peristaltic Pumps Transporting Rigid Particles in Stokes Flow
- Source :
- SIAM Journal on Scientific Computing, SIAM Journal on Scientific Computing, 2023, 45 (1), pp.B78-B106. ⟨10.1137/21M144863X⟩
- Publication Year :
- 2023
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2023.
-
Abstract
- This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a prescribed volume of fluid, number of particles and/or distance traversed by the particles over a set time period. Our approach relies on a recently developed fast and accurate boundary integral solver for simulating multiphase flows through periodic geometries of arbitrary shapes. In order to fully capitalize on the dimensionality reduction feature of the boundary integral methods, shape sensitivities must ideally involve evaluating the physical variables on the particle or pump boundaries only. We show that this can indeed be accomplished owing to the linearity of Stokes flow. The forward problem solves for the particle motion in a slip-driven pipe flow while the adjoint problems in our construction solve quasi-static Dirichlet boundary value problems backwards in time, retracing the particle evolution. The shape sensitivities simply depend on the solution of one forward and one adjoint (for each shape functional) problems. We validate these analytic shape derivative formulas by comparing against finite-difference based gradients and present several examples showcasing optimal pump shapes under various constraints.<br />Comment: 24 pages, 8 figures
- Subjects :
- Physics::Fluid Dynamics
integral equations
Computational Mathematics
fast algorithms
Optimization and Control (math.OC)
Applied Mathematics
FOS: Mathematics
Shape sensitivity analysis
particulate flows
Mathematics - Optimization and Control
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Subjects
Details
- ISSN :
- 10957197 and 10648275
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Scientific Computing
- Accession number :
- edsair.doi.dedup.....61713858dbb7ca1875390030d1855060