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J Comput Phys. 2015 Aug 15;297:182-193. Epub 2015 May 19.

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

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Department of Mathematics and CRSC, North Carolina State University, Raleigh, NC 27695, USA.
Departments of Biomedical Engineering and Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA.
Department of Mathematics, University of California, Irvine, CA 92697, USA.
Departments of Molecular Biology and Biochemistry, Chemical Engineering and Materials Science, and Biomedical Engineering, University of California, Irvine, CA 92697, USA.


In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.


Augmented immersed interface method (IIM); Finite difference approximation; Irregular domain; Local pressure boundary condition; Navier–Stokes equations; Open and traction boundary conditions

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