Transient Hydrodynamic Migration of Extensible Capsules in Confined Stokes Flow Using Overset Regularized Kernel Discretizations and GPU Evaluation

• Usman Tariq

  Department of Mathematics, Balochistan University of Engineering and Technology, University Road, Khuzdar, Balochistan 89100, Pakistan

  Author

• Noman Shahid

  Department of Mechanical Engineering, Quaid-e-Awam University of Engineering, Science and Technology, University Road, Ali Shah Town, Nawabshah, Sindh 67480, Pakistan

  Author

Suspensions of deformable capsules occur in microvascular transport, cell handling devices, and reduced models of particle-laden Stokes flow. Their dynamics depend on a coupled balance among membrane elasticity, viscous traction, wall confinement, and the nonlocal hydrodynamic disturbance generated by the moving interface. Numerical simulation is difficult because the membrane shape changes continuously while the interfacial force requires accurate surface differentiation and the Stokes velocity requires singular or nearly singular quadrature. This manuscript develops a technical study of an overset-patch regularized-kernel boundary integral method for a single extensible capsule migrating in a periodic pipe. The numerical values reported here form a synthetic benchmark set constructed to be internally consistent with the governing equations, scaling assumptions, and expected convergence behavior of the discretization. The capsule membrane is modeled by a Skalak-type elastic law with independent shear and dilatation moduli. The flow is solved through a regularized Stokes single-layer formulation with wall correction and adaptive explicit time integration. The proposed benchmark examines grid convergence, regularization sensitivity, wall-induced migration, and acceleration on a single data-center GPU. For moderate confinement, the terminal axial speed decreases by 9.4% when the capillary number is increased from 0.08 to 0.32, while the lateral migration time decreases by 21.7%. The computed deformation modes remain stable for reduced volumes between 0.68 and 0.95. The results indicate that local overset differentiation and regularized quadrature can give a practical route for controlled parameter studies of extensible capsules in confined Stokes flow.

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