The Immersed Interface Method for the Navier–Stokes Equations with Singular Forces
نویسندگان
چکیده
منابع مشابه
The Immersed Interface Method forthe Navier–Stokes Equationswith Singular Forces
Peskin’s Immersed Boundary Method has been widely used for simulating many fluid mechanics and biology problems. One of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain. However, the Immersed Boundary Method is known to be first-order accurate and usually smears out the soluti...
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In this paper, we introduce a simple version of immersed interface method (IIM) for the Stokes flow with singular forces along an interface. The numerical method is based on applying the Taylor’s expansions along the normal direction and incorporating the solution and its normal derivative jumps into the finite difference approximations. The numerical results show that the scheme is second-orde...
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The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in which there is an irregular surface F of codimension contained in fl across which , a, and f may be discontin...
متن کاملSingular forces in the immersed interface method for rigid objects in 3D
∧ for determining the singular force for the boundary of a rigid objectwith prescribedmotion in 2D [Sheng Xu, The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow, J. Comput. Phys. 227 (2008) 5045–5071]. ∧ Necessary formulas for extending the approach to 3D ∧ are derived in this ∧ work. With the implementation of these formulas, the i...
متن کاملA simple implementation of the immersed interface methods for Stokes flows with singular forces
In this paper, we introduce a simple version of the immersed interface method (IIM) for Stokes flows with singular forces along an interface. The numerical method is based on applying the Taylor’s expansions along the normal direction and incorporating the solution and its normal derivative jumps into the finite difference approximations. The fluid variables are solved in a staggered grid, and ...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2001
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6813