Multigrid algorithms for compressible flow calculations

Jameson, Antony

doi:10.1007/bfb0072647

Cited by 148 publications

(106 citation statements)

References 43 publications

(53 reference statements)

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“…The Fourier analysis of the multilevel scheme requires careful tracking of the transfer of residuals and corrections between the meshes. It is shown in reference [52] that ths amplification factor of the composite scheme can be expressed by a recursion formula.…”

Section: The Results W (M)mentioning

confidence: 99%

Computational transonics

Jameson

1988

Comm Pure Appl Math

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Section: The Results W (M)mentioning

confidence: 99%

Computational transonics

Jameson

1988

Comm Pure Appl Math

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“…This allows for acceleration techniques such as local time-stepping and multigrid strategies [36,37] to be employed. Since the solution is marched in time from the initial free-stream values to the final solution by constructing the time history of the flow, the method is deemed time-accurate (or time-marching).…”

Section: Frequency-domain Solution Methodsmentioning

confidence: 99%

“…The parameters for α p and β p are chosen as listed in Table 2-1, in order to be optimized for multigrid computations [8]. In order to further accelerate the convergence to the steady-state periodic solution, a W-cycle multigrid strategy [36,37] is employed in conjunction with a local [40]. Characteristic boundary conditions using one-dimensional Riemann invariants are used at the far-field boundary [40] whereas, at the body surface, the normal flow velocity is required to be zero and the pressure is determined through a linear extrapolation of the flow field pressure from the adjacent cells.…”

Section: Pseudotime-stepping Schemementioning

confidence: 99%

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

Tardif

Nadarajah

2017

AIAA Journal

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“…Coarser meshes are obtained by eliminating every other mesh line in each coordinate direction. The grid transfer operators for the solution, residual, and coarse grid corrections are those introduced by Jameson [15]. In particular, on the auxiliary meshes, the solution is initialized as…”

Section: Multigrid Methodsmentioning

confidence: 99%

An effective multigrid method for high‐speed flows

Swanson

Turkel

White

1992

Commun. appl. numer. methods

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We consider the use of a multigrid method with central differencing to solve the Navier-Stokes equations for high-speed flows. The time-dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two-dimensional lamipar flow over a circular cylinder and a 15 degree compression ramp. iI IntroductionDuring the 1980's a wide variety of numerical schemes were investigated for solving the Euler and Navier-Stokes equations. Multistage time-stepping schemes with central differencing and multigrid acceleration [1,2,3] were demonstrated to be quite effective in computing subsonic and transonic flows 'ver aerodynamic components and configurations. With the recent resurgence of interest in high-speed flight vehicles, we now need to construct versatile algorithms for hypersonic flow. One must keep in mind that hypersonic flows represent a formidable challenge for any flow solver. I1 particular, strong shock and expansion waves can occur in the flow field, and the3 can interact with each other and with shear layers (i.e., boundary layers, jets, wakes). Such strong nonlinear behavior and interactions can easily cause divergence of any numerical integration procedure. This is especially true during the initial phase of a calculation with a time-dependent method. So even the most successful algorithms of the last decade may require significant modifications to be effective for hypersonic flows.An initial effort [4] to apply a central-difference multigrid algorithm to high-speed flows resulted in numerical difficulties that prevented the calculation of two-dimensional flows (i.e., blunt body and wedge type) with a Mach number higher than about 7. In order to compute such flows a low Courant-Friedrichs-Lewy (CFL) number was required. Thus four and five stage schemes were not practical, since there is substantial deterioration in the high frequency damping of the scheme due to the large reduction in the CFL number. The CFL restriction reduced the potential of the scheme as a viscous flow solver. More recently an algorithm utilizing a semicoarsening technique, a symmetric TVD formulation, and a three stage Runge-Kutta scheme [5] was proposed and used to compute high Reynolds number (laminar) Mach 10 flow over an airfoil at 10 degrees angle of attack. A good resolution of the bow shock wave and a reasonable convergence rate were obtained. The method of semicoarsening considered required a much more complicated cycle strategy than that employed with standard multigrid methods. In addition, it appears to be somewhat cumbersome to implement in three dimensions.It is our contention that standard multigrid techniques can be u:.,d in conjunction with central differencing to compute hypersonic flows effectively. To achieve such success with these techniques ...

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Multigrid algorithms for compressible flow calculations

Cited by 148 publications

References 43 publications

Computational transonics

Computational transonics

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

An effective multigrid method for high‐speed flows

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