A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions. (English) Zbl 1349.76498
Summary: 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.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76Z05 | Physiological flows |
| 92C35 | Physiological flow |
Keywords:
Navier-Stokes equations; finite difference approximation; irregular domain; open and traction boundary conditions; local pressure boundary condition; augmented immersed interface method (IIM)References:
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