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Computing Viscous Flow Along a 2D Open Channel Using the Immersed Interface Method
  • Sarah Patterson,
  • Anita Layton
Sarah Patterson
Virginia Military Institute
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Anita Layton
University of Waterloo
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We present a numerical method for simulating 2D flow through a channel with deformable walls. The fluid is assumed to be incompressible and viscous. We consider the highly viscous regime, where fluid dynamics are described by the Stokes equations, and the less viscous regime described by the Navier-Stokes equations. The model is formulated as an immersed boundary problem, with the channel defined by compliant walls that are immersed in a larger computational fluid domain. The channel traverses through the computational domain, and the walls do not form a closed region. When the walls deviate from their equilibrium position, they exert singular forces on the underlying fluid. We compute the numerical solution to the model equations using the immersed interface method, which preserves sharp jumps in the solution and its derivatives. The immersed interface method typically requires a closed immersed interface, a condition that is not met by the present configuration. Thus, a contribution of the present work is the extension of the immersed interface method to immersed boundary problems with open interfaces. Numerical results indicate that this new method converges with second-order accuracy in both space and time, and can sharply capture discontinuities in the fluid solution.

Peer review status:Published

20 Jan 2020Submitted to Engineering Reports
23 Jan 2020Submission Checks Completed
23 Jan 2020Assigned to Editor
13 May 2020Reviewer(s) Assigned
22 Jun 2020Editorial Decision: Revise Major
31 Oct 20201st Revision Received
31 Oct 2020Submission Checks Completed
31 Oct 2020Assigned to Editor
02 Nov 2020Editorial Decision: Accept
10 Dec 2020Published in Engineering Reports. 10.1002/eng2.12334