A Simple 3D Immersed Interface Method for Stokes Flow with Singular Forces on Staggered Grids
نویسندگان
چکیده
منابع مشابه
A Simple Immersed Interface Method for the Stokes Flow with Singular Forces
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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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 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 ...
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...
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We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) near the interface using the immersed interface method, adding terms related to the jumps, on a regular gri...
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ژورنال
عنوان ژورنال: Communications in Computational Physics
سال: 2022
ISSN: ['1991-7120', '1815-2406']
DOI: https://doi.org/10.4208/cicp.oa-2020-0137