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Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Journal of Hydrodynamics 2016年第5期28卷 713-730页

作者： Jianming YANG Fidesi Solutions LLC PO Box 734 Iowa City IA 52244 USA

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

关键词： immersed boundary methods direct forcing sharp interface method strong coupling schemes fluid-structureinteractions cartesian grid methods

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The Immersed Interface Method for Simulating Two-Fluid Flows

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Numerical Mathematics(Theory,methods and Applications) 2014年第4期7卷 447-472页

作者： Miguel Uh Sheng Xu Department of Mathematics Southern Methodist UniversityDallasTX 75275-0156USA

We develop the immersed interface method(IIM)to simulate a two-fluid flow of two immiscible fluids with different density and viscosity.Due to the surface tension and the discontinuous fluid properties,the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface separating the two fluids.The IIM computes the flow on a fixed cartesian grid by incorporating into numerical schemes the necessary jump conditions induced by the interface.We present how to compute these necessary jump conditions from the analytical principal jump conditions derived in[Xu,DCDS,Supplement 2009,pp.838-845].We test our method on some canonical two-fluid flows.The results demonstrate that the method can handle large density and viscosity ratios,is second-order accurate in the infinity norm,and conserves mass inside a closed interface.

关键词： Immersed interface method two-fluid flows jump conditions augmented variable approach singular force cartesian grid methods

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