A locally implicit scheme for the Euler equations

Reddy, K. Suresh Kumar; Jacocks, J L

doi:10.2514/6.1987-1144

Cited by 15 publications

(13 citation statements)

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“…It does not require the assembly of any global matrices and does not need any matrix system solvers. The locally implicit scheme is originally developed by Reddy and Jacock [31] on structured quadrilaterals. Hwang and Liu [30] developed the locally implicit scheme and anisotropic dissipation model on the static triangular mesh.…”

Section: Governing Equationsmentioning

confidence: 99%

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Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

Yang

2003

Numerical Methods in Fluids

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SUMMARYAn error indicator and a locally implicit scheme with anisotropic dissipation model on dynamic quadrilateral-triangular mesh are developed to study transonic ows over vibrating blades with interblade phase angles. In the Cartesian co-ordinate system, the unsteady Euler equations with moving domain e ects are solved. The error indicator, in which uniÿed magnitudes of dynamic grid speed, substantial derivative of pressure, and substantial derivative of vorticity magnitude are incorporated to capture the unsteady wave behaviours and vortex-shedding phenomena due to unsteadiness. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two ow calculations are performed. Based on the comparison with the related numerical and experimental data, the accuracy of the present approach is conÿrmed. According to the high-resolutional result on the adaptive mesh, the unsteady pressure wave, shock and vortex-shedding behaviours are clearly demonstrated.

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Section: Governing Equationsmentioning

confidence: 99%

“…To solve Equation (6), a locally implicit scheme [31,32] is implemented. This scheme is locally implicit, but globally explicit and is unconditionally stable under local linearized analysis [32].…”

Section: Governing Equationsmentioning

confidence: 99%

Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

Yang

2003

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…It does not require the assembly of any global matrices and does not need any matrix system solvers. The locally implicit scheme is originally developed by Reddy and Jacock [24] on structured quadrilaterals. Hwang and Liu [25] developed the locally implicit scheme and anisotropic dissipation model on a triangular mesh.…”

Section: Governing Equationsmentioning

confidence: 99%

“…To solve Equation (7), a locally implicit scheme [24,30] is implemented. This scheme is locally implicit, but globally explicit and is unconditionally stable under local linearized analysis [30].…”

Section: Governing Equationsmentioning

confidence: 99%

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Adaptive strategy of the supersonic turbulent flow over a backward‐facing step

Yang

2004

Numerical Methods in Fluids

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SUMMARYAn adaptive strategy incorporating mesh remeshing and reÿning is developed to study the supersonic turbulent ow over a backward-facing step on a mixed quadrilateral-triangular mesh. In the Cartesian co-ordinate system, the unsteady Favre-averaged Navier-Stokes equations with a low-Reynolds-number k-turbulence model are solved using a locally implicit scheme with an anisotropic dissipation model. In the present adaptive strategy, two error indicators for both mesh remeshing and reÿning, respectively, are presented. The remeshing error indicator incorporates uniÿed magnitude of substantial derivative of pressure and that of vorticity magnitude, whereas the reÿning error indicator incorporates uniÿed magnitude of substantial derivative of pressure and that of weighted vorticity magnitude. To assess the present approach, the transonic turbulent ow around an NACA 0012 airfoil is performed. Based on the comparison with the experimental data, the accuracy of the present approach is conÿrmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

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The application of the locally implicit method to upwind TVD schemes

Jeng

Payne

1992

J Sci Comput

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A locally implicit scheme for the Euler equations

Cited by 15 publications

References 0 publications

Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

Adaptive strategy of the supersonic turbulent flow over a backward‐facing step

The application of the locally implicit method to upwind TVD schemes

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