A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains

  • Authors:

  • Kazufumi Ito;Ming-Chih Lai;Zhilin Li

  • Affiliations:

  • Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States;Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 30050, Taiwan;Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

An augmented method based on a Cartesian grid is proposed for the incompressible Navier-Stokes equations in irregular domains. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be utilized in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results in an ill-conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improves the condition number of the system for the augmented variable significantly. Using the immersed interface method, we are able to achieve second order accuracy for the velocity. Numerical results and comparisons to benchmark tests are given to validate the new method. A lid-driven cavity flow with multiple obstacles and different geometries are also presented.