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Numerical Simulation Using High-Resolution Methods

Numerical Simulation Using High-Resolution Methods. A. D. Weatherhead, AWE D. Drikakis, Cranfield University. Aims. To validate a well tested code in a new regime. To assess the behaviour of different numerical methods on Rayleigh-Taylor turbulent mix. Summary. The two codes CNS3D

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Numerical Simulation Using High-Resolution Methods

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  1. Numerical Simulation Using High-Resolution Methods A. D. Weatherhead, AWE D. Drikakis, Cranfield University

  2. Aims • To validate a well tested code in a new regime. • To assess the behaviour of different numerical methods on Rayleigh-Taylor turbulent mix

  3. Summary • The two codes • CNS3D • Turmoil • Gravity • Rising Bubble • Rayleigh-Taylor Simulation • Single Mode RT • Multi Mode RT • Conclusions

  4. CNS3D Cranfield University’s compressible code developed by D.Drikakis Validated using: Aerodynamic flows Wing dynamics Transonic atmosphere re-entry Turmoil AWE scientific research code developed by D.Youngs Validated using: Turbulence modeling Rocket rig experiments Shock tube experiments The Two Codes

  5. Cell centered finite volume code Range of Riemann solvers: Eberle HLLC Roe Numerous limiting methods: Van Leer Superbee Kim&Kim 5thOrder MUSCL WENO CNS3D density momentum total energy

  6. Staggered grid Finite difference Lagrange re-map Turmoil velocity velocity velocity density internal energy velocity velocity velocity

  7. Rising Bubble • The bubble rise test problem originated from a paper by A S Almgren et al [i] in which they are modelling the rise of hot bubbles in type Ia supernovae. The problem is interesting because it does not have a hard boundary to the bubble and as such in the initial conditions all of the variables are smoothly varying. Having smoothly varying initial conditions should mean that the results are not significantly dependent on the limiter used. • [i] A S Almgren, J B Bell, C A Rendleman and M Zingale, “LOW MACH NUMBER MODELING OF TYPE Ia SUPERNOVAE. I. HYDRODYNAMICS”, The Astrophysical Journal, 637:922, 936 (2006)

  8. High Mach Results CNS3D Turmoil

  9. Low Mach Results CNS3D Turmoil

  10. Rayleigh-Taylor Instability • Light fluid with higher pressure • Minor perturbations are unstable

  11. Single Mode RT • This test problem is a simple single mode Rayleigh-Taylor calculation based on the single mode studies carried out by the a group [1]. • The problem consist of a rectangular box with a heavy fluid (r=3g/cm3) above a light fluid (r=1g/cm3), both at rest, in a gravitational field. • There is a single mode perturbation on the interface that develops to form a bubble in the centre and spikes at the corners of the box.

  12. Turmoil VanLeer Superbee 3D WENO Single Mode 3D Results • This test problem is very sensitive to the numerical scheme used. • Important points to look out for are the amount of roll up in the spikes and height and shape of the top of the bubble. • A dimple or quartering of the bubble often appears with the less diffusive schemes.

  13. Results – 2D Slices Turmoil WENO 3rd Order 3D WENO 3rd Order Van Leer 3D WENO 3rd Order 2 x resolution Van Leer 2 x resolution WENO 5th Order 2 x resolution Superbee

  14. High Resolution Turmoil WENO 5th 3D WENO Van Leer MUSCL5th

  15. Multi Mode RT • The multimode calculations were carried out using the 128x128x128 initial conditions used by the alpha group [19]. The domain for the multimode calculations was 10.0 x 10.0 x 10.0 and was meshed with a uniform mesh of 128 cells in each direction. The density ratio is initially 3 to 1. Both the density and pressure have been adjusted to give hydrostatic equilibrium. The initial interface has been perturbed using the following equation: h0(x,y) = S ( ak cos(kxx)cos(kyy)+bk cos(kxx)sin(kyy) +ck sin(kxx)cos(kyy)+dk sin(kxx)sin(kyy)) • where the sum is over all wavenumbers and spectral amplitudes (ak, bk, ck, dk) are chosen randomly.

  16. 3D Results Turmoil 5th Order WENO Van Leer Superbee

  17. Initial Conditions Van Leer Van Leer Van Leer Wavelengths: 4cells to 16cells Wavelengths: 8cells to 32cells Wavelengths: 16cells to 64cells

  18. Resolution Van Leer 2563 Van Leer 1283

  19. Conclusion • Different codes and methods agree on the macroscope behaviour. • Numerical methods have a significant affect on the details of the calculations. • The differences between the methods are more significant at low mach number. • Low mach number modifications can significantly improve the behaviour.

  20. Results – 2D Slices ENO 2nd Order Van Leer Turmoil Minbee Van Leer 2 x resolution WENO 3rd Order WENO 5th Order 2 x resolution Minbee N=2 Van Albada 3D WENO 3rd Order 2 x resolution Van Albada N=3 Minbee N=4 3D WENO 3rd Order Van Albada N=20 Superbee

  21. 3D Results Van Leer NEPS=20 Van Leer NEPS=3 Turmoil 3D WENO

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