Higher-order and 3-D finite element methods for the Euler equations

Shapiro, Richard A.; Murman, Earll M.

doi:10.2514/6.1989-655

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…This is due primarily to the shift of emphasis from steady inviscid Euler flow simulations toward accurate simulations of time-dependent, viscous flows (see [1,2]). Also, new fields such as computational electromagnetics for aerospace design involve the solution of time-dependent highly oscillatory solutions for which high-order discretization is more efficient [3].…”

Section: Introductionmentioning

confidence: 99%

Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

Lomtev¹,

Quillen²,

Karniadakis³

1998

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

Lomtev¹,

Quillen²,

Karniadakis³

1998

Journal of Computational Physics

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“…The range of applicability of the implicit procedure is demonstrated by describing its use, on general adapted unstructured grids, in the solution of laminar viscous flow at transonic speed over an aerofoil and at hypersonic speed past a double ellipse configuration. l 3 We have previously' proposed to solve three-dimensional viscous flows by initially laying down a grid of tetrahedra which is structured only in the normal direction in the vicinity of solid surfaces and to employ a totally unstructured grid elsewhere. An implicit/explicit solution algorithm for the Navier-Stokes equations was then employed with the explicit form being used on the unstructured portion of the mesh and the implicit form being used in the structured region.…”

Section: Introductionmentioning

confidence: 99%

An implicit finite‐element method for high‐speed flows

Hassan¹,

Morgan²,

Peraire³

1991

Numerical Meth Engineering

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SUMMARYA fast algorithm is presented for constructing continuous lines, made up of element sides, which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions. The lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two-dimensional problems of steady compressible inviscid and laminar viscous high-speed flows, where the equation system is solved by line relaxation using a block tridiagonal equation solver. For three-dimensional laminar viscous simulations it is proposed to utilize an implicitlexplicit finite-element formulation. In the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while, away from this region, the grid will be totally unstructured. In the structured region, lines in the normal direction to the wall are readily identified, while lines in the surfaces parallel to the solid wall are constructed using the proposed two-dimensional procedure. The implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation. An explicit form of the solution algorithm is used elsewhere. To illustrate the performance of the proposed method, solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions. The application of the proposed procedure to the solution of three-dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described.

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Perspective on unstructured grid flow solvers

Venkatakrishnan

1996

AIAA Journal

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Higher-order and 3-D finite element methods for the Euler equations

Cited by 4 publications

References 7 publications

Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

An implicit finite‐element method for high‐speed flows

Perspective on unstructured grid flow solvers

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