Design of optimally smoothing multistage schemes for the euler equations

Leer, Bram van; Lee, Wen-Tzong; Roe, Philip L.; Powell, Kenneth G.; Tai, Chang-Hsien

doi:10.1002/cnm.1630081006

Cited by 55 publications

(28 citation statements)

References 11 publications

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“…6 is solved using multi-stage explicit time-marching schemes [54] in conjunction with global or local time steps obeying the Courant-Friedrichs-Lewy (CFL) stability condition. The source term in the discrete Eq.…”

Section: Explicit Temporal Discretization Methodsmentioning

confidence: 99%

High-order central ENO finite-volume scheme for ideal MHD

Susanto

Ivan

Sterck

et al. 2013

Journal of Computational Physics

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A high-order central essentially non-oscillatory (CENO) finite-volume scheme is developed for the compressible ideal magnetohydrodynamics (MHD) equations solved on threedimensional (3D) cubed-sphere grids. The proposed formulation is an extension to 3D geometries of a recent high-order MHD CENO scheme developed on two-dimensional (2D) grids. The main technical challenge in extending the 2D method to 3D cubed-sphere grids is to properly handle the nonplanar cell faces that arise in cubed-sphere grids. This difficulty is solved by considering general hexahedral cells with trilinear faces, which allow us to compute fluxes, areas and volumes with high-order accuracy by transforming to a reference cubic cell. The 3D CENO scheme is implemented within a flexible multi-block cubed-sphere grid framework to fourth-order accuracy, resulting in a high-order solution method for cubed-sphere grids with unique capabilities in terms of adaptive refinement and parallel scalability. The high-order method is applicable to the solution of general hyperbolic conservation laws with, in principle, arbitrary order. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions, even for smooth extrema, and non-oscillatory transitions at discontinuities. The scheme is applied herein to MHD in combination with a GLM divergence correction technique to control the solenoidal condition for the magnetic field while preserving the high-order accuracy of the numerical procedure. The cubed-sphere simulation framework features a flexible design based on a genuine multi-block implementation, leading to high-order accuracy, flux calculation, adaptivity and parallelism that are fully transparent to the boundaries between the six sectors of the cubedsphere grid. The proposed 3D MHD CENO scheme is shown to achieve uniform fourth-order accuracy on cubed-sphere grids. Parallel domain partitioning and grid adaptivity are achieved on the 3D cubed-sphere grids using a hierarchical block-based division strategy with blocks of equal size. Numerical results to demonstrate the high-order accuracy, robustness and capability of the proposed high-order framework are presented and discussed for several test problems.

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Section: Explicit Temporal Discretization Methodsmentioning

confidence: 99%

High-order central ENO finite-volume scheme for ideal MHD

Susanto

Ivan

Sterck

et al. 2013

Journal of Computational Physics

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“…Unless indicated otherwise, a (5, 5) RK scheme (numerical dissipation evaluated on all stages) is employed for all dissipation formulations considered for the residual function, and the RK coefficients are given by These coefficients were obtained from Ref. 31.…”

Section: Rk/implicit Schemementioning

confidence: 99%

Convergence Acceleration for Multistage Time-Stepping Schemes

Swanson

Turkel

Rossow

et al. 2006

36th AIAA Fluid Dynamics Conference and Exhibit

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The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 × 10 6 and 100.0 × 10 6 . Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, it is demonstrated that the computational time of a well-tuned standard RK scheme can be reduced at least a factor of four.

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“…An optimally damped 2 nd order scheme using five Runge-Kutta stages was used to compute the present set of subsonic cases [6]. The flow solver also uses multi-grid convergence acceleration to damp the high frequency error modes.…”

Section: Methodsmentioning

confidence: 99%

Computation of external aerodynamics for a canard rotor/wing aircraft

Pandya

Aftosmis

2001

39th Aerospace Sciences Meeting and Exhibit

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The aerodynamic loads on a Canard Rotor/14_ng vehicle are investigated using inviscid numerical simulations in order to understand the flight characteristics of the vehicle during conversion from rotor craft to foced-wing fiight. A series of numerical simulations at seven azimuthal rotor indices are presented covering a quarter turn of the rotor, l_th symmetry arguments, these simulations produce 25 data points for a complete rotation. A Cartesian mesh approach is used to compute the flow field about a configuration with faired-over engine inlet and exhaust that matches the wind tunnel geometry. These simulations were performed using meshes with approximately 9Million Cartesian cells. To better understand the aerodynamic effects of the rotor hub on the configuration, the same set of simulations were repeated for a hub-less geometry. Overall loads for both configurations are similar, but are due to somewhat different aerodynamic mechanisms.

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Design of optimally smoothing multistage schemes for the euler equations

Cited by 55 publications

References 11 publications

High-order central ENO finite-volume scheme for ideal MHD

High-order central ENO finite-volume scheme for ideal MHD

Convergence Acceleration for Multistage Time-Stepping Schemes

Computation of external aerodynamics for a canard rotor/wing aircraft

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