A zonal approach to solution of the Euler equations

Hessenius, Kristin A.; Pulliam, Thomas H.

doi:10.2514/6.1982-969

Cited by 16 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, techniques that employ non-overlapping grids (sometimes called patched grids) were developed. 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].…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Benek et al, 20 Hessenius and Pulliam, 21 Rai, 22 Hessenius and Rai, 23 and Dougherty et al 24 have used different types of zonal-grid approaches for solving the Euler equations. Benek et al, 20 Hessenius and Pulliam, 21 Rai, 22 Hessenius and Rai, 23 and Dougherty et al 24 have used different types of zonal-grid approaches for solving the Euler equations.…”

Section: And Srinivasan Andmentioning

confidence: 99%

Navier-Stokes Computations About Complex Configurations Including a Complete F-16 Aircraft

Holst

Flores²,

Chaderjian³

et al. 1990

Applied Computational Aerodynamics

View full text Add to dashboard Cite

IntroductionC OMPUTATIONAL fluid dynamics (CFD) algorithm and computer hardware developments have been rapidly advancing over the last decade. CFD computer codes have been used in many applications to improve the design of aircraft. For example, linear panel methods have been used to improve the design of complex aircraft configurations providing the flow does not contain shock waves or significant separation. Nonlinear potential methods have been used to remove the adverse characteristics caused by shock waves in the transonic regime with the limitation that vorticity and entropy production are not large. The problem of solving the Euler/Navier-Stokes equations about reasonably complete aircraft configurations is now the central issue facing the CFD research community, and, in fact, many significant results demonstrating the power of this approach have already been produced.There are many reasons for pursuing this line of research. First, the large computer costs associated with the numerical solution of the Euler/Navier-Stokes equations in three dimensions is rapidly decreasing. This is a direct result of new improved algorithms and fast vector computers such as the Cray XMP and YMP, the Cray 2, and the CDC Cyber 205. Second, there Downloaded by UNIVERSITY OF NEW SOUTH WALES on July 30, 2015 | http://arc.aiaa.org | Downloaded by UNIVERSITY OF NEW SOUTH WALES on July 30, 2015 | http://arc.aiaa.org | Downloaded by UNIVERSITY OF NEW SOUTH WALES on July 30, 2015 | http://arc.aiaa.org | Downloaded by UNIVERSITY OF NEW SOUTH WALES on July 30, 2015 | http://arc.aiaa.org | Downloaded by UNIVERSITY OF NEW SOUTH WALES on July 30, 2015 | http://arc.aiaa.org |

show abstract

“…The early studies of multi-block strategies include those of Atta (1981), Hessenius and Pulliam (1982), Rai and Chakravarthy (1984), Rai (1986, andRai (1986), among others. The application of different overlapping zonal grids for solving full-potential equations was investigated by Atta (1981) to obtain the transonic flow field about complex configurations (see also Atta and Vadyak, 1982;Benek et al 1983).…”

Section: Introductionmentioning

confidence: 99%

“…The computed results around a two-dimensional (2D) airfoil configuration showed an accurate and stable scheme, and overall, led to reduced computational costs. Hessenius and Pulliam (1982) presented a conservative block interface condition for solving one-and twodimensional Euler equations with implicit schemes. It was most importantly shown that the conservative treatment of boundary conditions at block interfaces is required for problems with discontinuities, e.g., shock waves.…”

Section: Introductionmentioning

confidence: 99%

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

2021

JAFM

View full text Add to dashboard Cite

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.

show abstract

A zonal approach to solution of the Euler equations

Cited by 16 publications

References 7 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

Navier-Stokes Computations About Complex Configurations Including a Complete F-16 Aircraft

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

Contact Info

Product

Resources

About