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Title page for ETD etd-06192014-150635


Type of Document Master's Thesis
Author Zhu, Chi
Author's Email Address chi.zhu@vanderbilt.edu
URN etd-06192014-150635
Title A high-order immersed-boundary method for simulation of incompressible flows
Degree Master of Science
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Haoxiang Luo Committee Chair
D. Greg Walker Committee Member
Prodyot K. Basu Committee Member
Keywords
  • high-order Poisson solver
  • least squares approximation
  • compact scheme
Date of Defense 2014-06-12
Availability unrestricted
Abstract
The use of immersed-boundary methods to solve complex/moving-boundary flow problems, especially those in biofluid dynamics, has been popular in recent years. Such methods typically employ a stationary structured grid, e.g., a Cartesian grid, for spatial discretization, so that grid generation is relatively simple and computation on the grid is efficient. However, existing immersed-boundary methods are usually up to second- order accurate. In this work, we have developed a high-order program to solve viscous, incompressible flows involving arbitrary boundaries by combining a fourth-order com- pact finite-difference scheme and a high-order immersed-boundary treatment based on least squares fitting. Moreover, a high-order compact scheme is developed to solve the pressure Poisson equation. In its discrete form, the new pressure solver can take ad- vantage of the same tri-diagonal structure as in the conventional second-order central finite-difference scheme, without introducing significant computational overhead.

Both model equations and Navier-Stokes equations have been tested using this method. First, we use one-dimensional numerical experiments to evaluate the feasibility of the method. Then, the complete two-dimensional program is used to solve both Kovasznay flow and flow past a circular cylinder to evaluate the performance of the program. These tests show that the high-order treatment of the immersed-boundary is compatible with the compact scheme. Furthermore, a third-order accuracy is achieved for the overall program as expected. In the end, application of the method for flapping wings is demonstrated.

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