A dual-time method for the solution of the
unsteady Euler equations

Gaitonde, Ann L

doi:10.1017/s0001924000026786

Cited by 65 publications

(39 citation statements)

References 3 publications

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“…The difference becomes most marked at the larger angles of incidence when the shock wave is present. The moment location which consistently gives closer comparison between inviscid computations and measured values is 0.273c [2,4,15,16]. However, for the current turbulent results, it was found that using the quoted experimental moment centre at 0.25c gives close agreement with experimental measurements.…”

Section: Test Casessupporting

confidence: 57%

Simulation of unsteady turbulent flows around moving aerofoils using the pseudo-time method

Badcock

Cantariti

Hawkins

et al. 2000

Int. J. Numer. Meth. Fluids

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Section: Test Casessupporting

confidence: 57%

Simulation of unsteady turbulent flows around moving aerofoils using the pseudo-time method

Badcock

Cantariti

Hawkins

et al. 2000

Int. J. Numer. Meth. Fluids

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“…Using a dual time-stepping method [62], backward differences are implicitly being used for the time derivatives. This means that the solution at each time level depends only upon the solution calculated at previous time levels.…”

Section: Flux-splittingmentioning

confidence: 99%

Conservative Unsteady Simulation of Arbitrary Motion in Two-dimensional Spacetime Using Central Difference, Upwind and Hybrid Formulations

Ederra

Rendall

Gaitonde

et al. 2017

23rd AIAA Computational Fluid Dynamics Conference

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms A spacetime framework is presented to solve unsteady aerodynamics problems as an alternative to conventional approaches for complex problems involving large deformation or topological change such as store separation, slat and flap deployment or spoiler deflection. It avoids complex CFD meshing methods, such as Chimera, by the use of a finite-volume approach both in space and time. The use of a central-difference scheme in the time direction yields non-physical transient solutions as a consequence of pressure waves travelling backwards in time. Therefore, an upwind formulation is provided and validated against one-dimensional test cases: a semi-infinite piston and a finite piston with a sharp change in direction. Also a hybrid formulation is given and several two-dimensional unsteady aerodynamics cases are computed with all three formulations and compared, demonstrating that the use of an upwind time stencil yields more representative physical solutions and improves the rate of convergence. In particular, the following problems are presented: a pitching NACA-0012 (periodic); a simple flap deflection; a spoiler deployment; a full landing case with a combination of slat, flap and spoiler deployments along with ground effect; and a case where aerofoils fly in opposite directions at subsonic and supersonic speeds.

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“…For time integration of equations used an implicit dual time method (Jameson 1991;Gaitonde 1994;Jahangirian and Hadidoolabi 2004), in real time a second order accurate backward difference formula (BDF) is used as follows…”

Section: Solution Algorithmmentioning

confidence: 99%

“…For time integration of equations used an implicit dual time method (Jameson 1991;Gaitonde 1994;Jahangirian and Hadidoolabi 2004). Considering the fixedness of the volume of elements in rotational motions of the body in the introduced grid, there is no need to calculate elements volume in every time step therefore the calculations decreases.…”

Section: Introductionmentioning

confidence: 99%

A 3-D Moving Mesh Method for Simulation of Flow around a Rotational Body

Razzaghi

Mirsajedi

2016

JAFM

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The numerical simulation of flow around a three dimensional moving body faces different problems in several methods, such as disruption of the structure of the grid, the need for deletion and insertion of nodes, interpolation, and data transfer between different parts of grid. In order to tackle the above-mentioned problems, a new configuration has been developed for meshing domain, which besides providing the body with the capability of rotational and oscillatory motions in large displacements, saves the grid's primitive quality. In the introduced method, the grid connections are manipulated with the motion of the body, but the general form of the grid is not changed or disrupted. This needs a special form for nodes of the grid, which is explained in this paper. The three dimensional unsteady form of the Euler equations is solved and the properties over each cell faces are evaluated using an averaging method. For time integration of the equations an implicit dual time method is used. It can prove that the volume of all elements is constant in the introduced grid. Therefore, there is no need to calculate elements volume in every time step. Several test cases are solved and the results are compared with experimental or other numerical data.

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A dual-time method for the solution of the unsteady Euler equations

Cited by 65 publications

References 3 publications

Simulation of unsteady turbulent flows around moving aerofoils using the pseudo-time method

Simulation of unsteady turbulent flows around moving aerofoils using the pseudo-time method

Conservative Unsteady Simulation of Arbitrary Motion in Two-dimensional Spacetime Using Central Difference, Upwind and Hybrid Formulations

A 3-D Moving Mesh Method for Simulation of Flow around a Rotational Body

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