Applications of a conservative zonal scheme to transient and geometrically complex problems

Hessenius, Kristin A.; M, M

doi:10.1016/0045-7930(86)90037-x

Cited by 17 publications

(6 citation statements)

References 2 publications

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“…Examples include a zonal approach that uses a flux-vector splitting technique for the determination of interface values in Euler equations [43,44,45,46], Lions method [19] that uses an iterative technique to arrive at the correct values to be passed between non-overlapping subdomains in solving Laplace's equation and more general second-order elliptic problems, Dawson's approach [9] that solves the heat equation using an explicit finite difference formula to determine the interface values and allows for different time stepping to be used in different subdomains. Non-overlapping grid techniques have also been extended and employed in solving the advection-diffusion equation [20] and the Navier-Stokes equations [45,22]. Some of the more recently developed non-overlapping domain decomposition methods achieve high finite global accuracy [47] and some spectral accuracy [21,7,48,22].…”

Section: Introductionmentioning

confidence: 99%

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

Merrill

Peet

Lottes

2016

Journal of Computational Physics

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An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrallyaccurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow-outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

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Section: Introductionmentioning

confidence: 99%

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

Merrill

Peet

Lottes

2016

Journal of Computational Physics

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“…Furthermore, Rai (1986) developed a conservative zonal-boundary scheme for the solution of Euler equations in which discontinuities were observed to smoothly move from one sub-domain to another through block boundaries. In a similar study, Hessenius and Rai (1986) also explored the interface treatments, based on the zonal-boundary scheme proposed by Rai (1986), for using with patched, discontinuous grid system around supersonic blunt bodies. The highorder interface treatment methodologies are broadly applied for the purpose of parallel processing (see Lien et al, 1996;Esfahanian et al, 2013;Morgan et al, 2001Morgan et al, , 2006.…”

Section: Introductionmentioning

confidence: 99%

A Block–Interface Approach for High–Order Finite–Difference Simulations of Compressible Flows

2021

JAFM

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The application of the high-order accurate schemes with multi-block domains is essential in problems with complex geometries. Primarily, accurate block-interface treatment is found to be of significant importance for precisely capturing discontinuities in such complex configurations. In the current study, a conservative and accurate multi-block strategy is proposed and implemented for a high-order compact finite-difference solver. For numerical discretization, the Beam-Warming linearization scheme is used and further extended for threedimensional problems. Moreover, the fourth-order compact finite-difference scheme is employed for spatial discretization. The capability of the high-order multi-block approach is then evaluated for the onedimensional flow inside a Shubin nozzle, two-dimensional flow over a circular bump, and three-dimensional flow around a NACA 0012 airfoil. The results showed a reasonable agreement with the available exact solutions and simulation results in the literature. Further, the proposed block-interface treatment performed quite well in capturing shock waves, even in situations that the location of the shock coincides with block interfaces.

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“…Rai [2][3][4] developed a conservative zonal-boundary scheme for grids having a common cellcentered line at the interface, which was later applied to study the two-dimensional stator/rotor interaction of an axial turbine stage [5]. Lerat and Wu [6] proposed a patched grid technique based on a common cell-side line instead.…”

Section: Introductionmentioning

confidence: 99%

Flux-conserving treatment of non-conformal interfaces for finite-volume discretization of conservation laws

2015

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We present a new flux-conserving treatment of non-conformal mesh block interfaces for the numerical solution of conservation laws by high order finite volumes schemes. An auxiliary mesh is used at the interface to establish a connectivity between non-conformal blocks. The method does not involve any flux interpolation and conservation is therefore guaranteed by construction, without enforcing additional constraints. Additionally, several gradient reconstructions across the interface have been adapted and their order of accuracy is studied analytically and numerically. Applications to two and three dimensional fluid dynamic problems are considered, and the verification of the method is provided by comparing solutions obtained on single-block grids with no interfaces. Also the accuracy and numerical stability of the interface treatment is demonstrated empirically for a variety of test cases, such as a cylinder in supersonic cross-flow, low Machnumber vortex shedding, and a transonic turbine stage. The exemplary flow simulation problems are solved using explicit and implicit time integration schemes. The obtained results successfully demonstrate the effectiveness of the proposed method for stationary non-conformal blocks domains, as well as for mesh blocks in relative motion.

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Applications of a conservative zonal scheme to transient and geometrically complex problems

Cited by 17 publications

References 2 publications

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

A Block–Interface Approach for High–Order Finite–Difference Simulations of Compressible Flows

Flux-conserving treatment of non-conformal interfaces for finite-volume discretization of conservation laws

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