A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. (English) Zbl 1134.76406
Summary: In the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on Cartesian grids is presented. In the proposed method an arbitrary three-dimensional solid surface immersed in the fluid is discretized using an unstructured, triangular mesh, and all the Cartesian grid nodes near the interface are identified. Then, the solution at these nodes is reconstructed via linear interpolation along the local normal to the body, in a way that the desired boundary conditions for both pressure and velocity fields are enforced. The overall accuracy of the resulting solver is second-order, as it is demonstrated in two test cases involving laminar flow past a sphere.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
References:
| [1] | Peskin, C. S., The immersed boundary method, Acta Numerica, 1-39 (2002) |
| [2] | Ye, T.; Mittal, R.; Udaykumar, H. S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., 156, 209-240 (1999) · Zbl 0957.76043 |
| [3] | Kirkpatrick, M. P.; Armfield, S. W.; Kent, J. H., A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid, J. Comput. Phys., 184, 1, 1-36 (2003) · Zbl 1118.76350 |
| [4] | Fadlun, E. A.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161, 35-60 (2000) · Zbl 0972.76073 |
| [5] | Kim, J.; Kim, D.; Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171, 132-150 (2001) · Zbl 1057.76039 |
| [6] | E. Balaras, Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations, Comput. Fluids (in press); E. Balaras, Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations, Comput. Fluids (in press) · Zbl 1088.76018 |
| [7] | Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, A.; Tauber, W.; Han, J.; Nas, S.; Jan, Y.-J., A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708-759 (2001) · Zbl 1047.76574 |
| [8] | Sotiropoulos, F.; Abdallah, S., The discrete continuity equation in primitive variable solutions of incompressible-flow, J. Comput. Phys., 95, 1, 212-227 (1991) · Zbl 0725.76058 |
| [9] | Sotiropoulos, F.; Ventikos, Y., Transition from bubble-type vortex breakdown to columnar vortex in a confined swirling flow, Int. J. Heat Fluid Flow, 19, 446-458 (1998) |
| [10] | Johnson, T.; Patel, V. C., Flow past a sphere up to a Reynolds number of 300, J. Fluid Mech., 378, 19 (1999) |
| [11] | T.A. Johnson, Numerical and experimental investigation of flow past a sphere up to a Reynolds number of 300, Ph.D. Dissertation, University of Iowa, 1996; T.A. Johnson, Numerical and experimental investigation of flow past a sphere up to a Reynolds number of 300, Ph.D. Dissertation, University of Iowa, 1996 |
| [12] | Thomson, J., Time-dependent boundary conditions for hyperbolic systems II, J. Comput. Phys., 89, 439-461 (1990) · Zbl 0701.76070 |
| [13] | Jeong, J.; Hussein, F., On the identification of a vortex, J. Fluid Mech., 285, 69 (1995) · Zbl 0847.76007 |
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