Nested Cartesian grid method in incompressible viscous fluid flow

Peng, Yih‐Ferng; Mittal, Rajat; Sau, Amalendu; Hwang, Robert R.

doi:10.1016/j.jcp.2010.05.041

Cited by 25 publications

(13 citation statements)

References 52 publications

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“…To conserve CPU time and memory storage, Peng et al [31] proposed a local grid refinement method (nested Cartesian grid method). Solutions of the global grid domain and the nested fine grid domain are solved through the use of some "ghost cells."…”

Section: Patch Grids and Numerical Implementationmentioning

confidence: 99%

“…Unlike in the nested Cartesian grid method proposed by Peng et al [31], no interpolation procedure is needed in the present study due to the fact that the black dots are the common grid points of the global and the patched grid systems. Based on these Dirichlet boundary conditions on the inner boundary, the flow field in the global grid system is solved with a conventional numerical method such as that described in section 2.…”

Section: Patch Grids and Numerical Implementationmentioning

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: Patch Grids and Numerical Implementationmentioning

confidence: 99%

Section: Patch Grids and Numerical Implementationmentioning

confidence: 99%

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

2017

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“…Popinet proposed the adaptive quad/octree Gerris solver, which uses a combination of an approximate projection approach and the multigrid method to numerically solve the time‐dependent incompressible Euler equations. A nested finite volume‐based Cartesian grid was presented by Peng et al to simulate unsteady viscous incompressible flows with complex immersed boundaries. The equations resulting from discretisation on structured grids were solved using an iterative method known as line‐successive‐over‐relaxation with a fast convergence rate.…”

Section: Introductionmentioning

confidence: 99%

“…Generally, linear interpolations to transfer data from coarse to fine grids are used for the prolongation process, and cell averaging procedures to reduce fine grid data onto coarse grids are used for the restriction process, and many fluid flow problems can be treated effectively using this technique. However, while the aforementioned studies focused on the simulation of laminar flows, the application of nested grids for turbulent flows, and in particular for LES/DNS, requires different, more sophisticated strategies to minimise (or ideally remove) the negative by‐products of grid discontinuities (in particular the inherent violation of conservativeness) on the accuracy and stability of the solution. Special interpolation algorithms, advanced numerical methods, higher‐order discretisations and variable filters have been applied in LES computations to circumvent these issues .…”

Section: Introductionmentioning

confidence: 99%

A local mesh refinement approach for large‐eddy simulations of turbulent flows

Cevheri

McSherry

Stoesser

2016

Numerical Methods in Fluids

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SUMMARYIn this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces.

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“…The separated operation allows the nonconforming mesh for the fluid domain, and the interface is implicit in these methods, which means the coupling information cannot be transmitted directly. [17][18][19][20] One difficulty with this method is that the deforming solid moves on the fixed grid causing various irregular cut cells because of the large number of intersections, and these cut cells require massive special treatments to avoid numerical errors. Cartesian methods and immersed-typed methods are 2 major kinds of non-boundary-fitted mesh methods in light of the enforcement of coupling condition.…”

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confidence: 99%

An immersed smoothed point interpolation method (IS‐PIM) for fluid‐structure interaction problems

Wang

Zhang

et al. 2017

Numerical Methods in Fluids

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Summary An immersed smoothed point interpolation method using 3‐node triangular background cells is proposed to solve 2D fluid‐structure interaction problems for solids with large deformation/displacement placed in incompressible viscous fluid. In the framework of immersed‐type method, the governing equations can be decomposed into 3 parts on the basis of the fictitious fluid assumption. The incompressible Navier‐Stokes equations are solved using the semi‐implicit characteristic‐based split scheme, and solids are simulated using the newly developed edge‐based smoothed point interpolation method. The fictitious fluid domain can be used to calculate the coupling force. The numerical results show that immersed smoothed point interpolation method can avoid remeshing for moving solid based on immersed operation and simulate the contact phenomenon without an additional treatment between the solid and the fluid boundary. The influence from information transfer between solid domain and fluid domain on fluid‐structure interaction problems has been investigated. The numerical results show that the proposed interpolation schemes will generally improve the accuracy for simulating both fluid flows and solid structures.

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Nested Cartesian grid method in incompressible viscous fluid flow

Cited by 25 publications

References 52 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

A local mesh refinement approach for large‐eddy simulations of turbulent flows

An immersed smoothed point interpolation method (IS‐PIM) for fluid‐structure interaction problems

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