A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains

Linnick, Mark Nicholas; Fasel, Hermann F.

doi:10.1016/j.jcp.2004.09.017

Cited by 308 publications

(181 citation statements)

References 34 publications

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“…Good agreements among the results are seen. The present numerical method seems to predict a drag coefficient that is slightly smaller than the existing numerical results [34][35][36]. This will be discussed later.…”

Section: Uniform Flow Past a Stationary Cylindermentioning

confidence: 61%

“…where ( ) k fp p is the desired pressure (35) and ˆk p  is the pressure solution of the previous iteration. …”

Section: The Implicit Virtual Boundary Methodsmentioning

confidence: 99%

“…For both cases of Re = 20 and Re = 40, there is a stable recirculation zone behind the cylinder that contains a pair of symmetric vortices. To examine the accuracy of the predicted wake structure, the present numerical results for the length of the recirculation zone l/D, distance from the cylinder to the centers of the vortices a/D, the gap between the centers of the vortices b/D, the separation angle θ s , and the drag coefficient C D are compared with that from the existing experimental and numerical studies [33][34][35][36] in Table 1. Good agreements among the results are seen.…”

Section: Uniform Flow Past a Stationary Cylindermentioning

confidence: 99%

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Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

2017

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A simple numerical method is proposed in the paper for fluid flow around a moving boundary of irregular shape. The unsteady term is discretized with the implicit scheme such that large time step is allowed. All of the computations are performed on non-staggered Cartesian grid system. Fine Cartesian patch grid system covering the moving object is employed to resolve the solution around the solid body. A closed curve defined by connecting the solid grid points adjacent to the solid-liquid interface is referred to as virtual boundary. The narrow irregular strip of solid between the virtual boundary and the actual solid-fluid interface is called pseudo-fluid. The general fluid region consisting of both fluid and pseudo-fluid is a regular domain that can be efficiently solved with conventional numerical method. In this connection, external force is imposed at each fluid grid point adjacent to the solid-fluid interface to compensate for the numerical error arising from the assumption of pseudo-fluid. The solution procedure is iterated until the required external force converges. Accuracy of the new numerical method is validated through three test problems. The numerical method then is used to investigate the flow induced by the flapping wings of a tethered dragonfly in literature. The corresponding CFL numbers of the four examples are infinity, 20, 100, and 3.29.

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Section: Uniform Flow Past a Stationary Cylindermentioning

confidence: 61%

“…where ( ) k fp p is the desired pressure (35) and ˆk p  is the pressure solution of the previous iteration. …”

Section: The Implicit Virtual Boundary Methodsmentioning

confidence: 99%

Section: Uniform Flow Past a Stationary Cylindermentioning

confidence: 99%

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Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

2017

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“…A relevant, while quite distinct approach is the integral equation method for complex geometry [44,45]. Aforementioned methods have found much success in scientific and engineering applications [6][7][8]15,18,20,[25][26][27][28]30,32,34,39,41,40,42,53,54,[57][58][59]. A possible further direction in the field could be the development of higher order interface methods [20,60,61] which are particularly desirable for problems involving both material interfaces and high frequency oscillations, such as the interaction of turbulence and shock, and high frequency wave propagation in inhomogeneous media [5].…”

Section: Introductionmentioning

confidence: 99%

Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces

Zhou

Guo

2007

Journal of Computational Physics

167

182

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Elliptic problems with sharp-edged interfaces, thin-layered interfaces and interfaces that intersect with geometric boundary, are notoriously challenging to existing numerical methods, particularly when the solution is highly oscillatory. This work generalizes the matched interface and boundary (MIB) method previously designed for solving elliptic problems with curved interfaces to the aforementioned problems. We classify these problems into five distinct topological relations involving the interfaces and the Cartesian mesh lines. Flexible strategies are developed to systematically extends the computational domains near the interface so that the standard central finite difference scheme can be applied without the loss of accuracy. Fictitious values on the extended domains are determined by enforcing the physical jump conditions on the interface according to the local topology of the irregular point. The concepts of primary and secondary fictitious values are introduced to deal with sharp-edged interfaces. For corner singularity or tip singularity, an appropriate polynomial is multiplied to the solution to remove the singularity. Extensive numerical experiments confirm the designed second order convergence of the proposed method.

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“…It is typically only first-order accurate in higher space dimensions. Some high order IB schemes have been proposed recently in the literature ( [15][16][17][18][19][20][21]). …”

Section: Introductionmentioning

confidence: 99%

A kernel-free boundary integral method for elliptic boundary value problems

Ying

Henriquez

2007

Journal of Computational Physics

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This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.

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A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains

Cited by 308 publications

References 34 publications

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces

A kernel-free boundary integral method for elliptic boundary value problems

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