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Related Experiment Videos

Numerical schemes for unsteady fluid flow through collapsible tubes.

D Elad1, D Katz, E Kimmel

  • 1Faculty of Engineering, Tel Aviv University, Israel.

Journal of Biomedical Engineering
|January 1, 1991
PubMed
Summary

Numerical schemes like Lax-Wendroff and MacCormack accurately solve one-dimensional incompressible flow in collapsible tubes. Stability and accuracy depend on viscous pressure loss from wall friction.

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Area of Science:

  • Fluid dynamics
  • Computational fluid dynamics
  • Biomechanics

Background:

  • Fluid flow in compliant tubes presents a fluid-structure interaction challenge.
  • Numerical methods for compressible flow in rigid ducts are analogous to this problem.
  • Investigating these methods for collapsible tube flow is crucial.

Purpose of the Study:

  • To evaluate the effectiveness of Lax-Wendroff and MacCormack schemes for one-dimensional incompressible flow in a straight collapsible tube.
  • To compare time-evolving numerical solutions with exact steady-state solutions.

Main Methods:

  • Application of Lax-Wendroff and MacCormack numerical schemes.
  • Simulation of one-dimensional incompressible flow through a straight collapsible tube.
  • Comparison of unsteady numerical results with exact steady-state solutions.

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Main Results:

  • The unsteady numerical solution converges with high accuracy to the exact steady-state solution when boundary conditions are fixed.
  • The stability and accuracy of both schemes are influenced by viscous pressure loss due to wall friction.
  • Flows exhibiting undamped oscillations were found to be unsolvable by these techniques.

Conclusions:

  • Lax-Wendroff and MacCormack schemes can accurately simulate steady-state conditions for incompressible flow in collapsible tubes.
  • Wall friction plays a critical role in the stability and accuracy of these numerical methods.
  • These methods are not suitable for analyzing flows with undamped oscillations.