Abstract
Dynamic interactions of shock waves and turbulent structures occur in a wide range of applications. The accurate simulation of turbulence in these flows requires a numerical scheme with minimal dissipation whereas the shock-capturing requires a dissipative scheme to stabilise the solution in the shock-wave discontinuous regions. These contradictory requirements make simulations of these flows extremely challenging. A compatible implementation of the solid boundary conditions at the point of incepting the acoustic waves and their internalisation into hydrodynamic instabilities is also challenging. Here we present, a high-fidelity, massively parallel and accurate solver for both direct numerical simulations and large-eddy simulations of supersonic turbulent flows in cylindrical coordinates. A hybrid WENO/ high order central difference scheme is used for the spatial discretisation with a fourth-order five-stage 2N-storage Runge–Kutta for the time integration. The least square contraction of Lilly [1] is utilised for large-eddy subgrid-scale modelling. The solid surface boundary condition is implemented using the offset wall and ghost cell technique. The numerical implementation is validated through a wide range of test cases from simple to more complex cases. The numerical results show good agreement with analytical solutions and available experimental results. In the large-eddy simulation of a supersonic under-expanded impinging jet, it is observed that the conventional Ducros sensor leads to a more dissipative hybrid scheme. In this paper, a new shock sensor based on a WENO smoothness indicator is proposed and it is demonstrated to perform better especially in the simulation of the supersonic under-expanded impinging jet by limiting the expensive WENO scheme to the discontinuous regions and reducing the computational cost by approximately 10%.
| Original language | English |
|---|---|
| Article number | 104241 |
| Number of pages | 14 |
| Journal | Computers and Fluids |
| Volume | 191 |
| DOIs | |
| Publication status | Published - 15 Sep 2019 |
Keywords
- Cylindrical coordinate
- Hybrid WENO/ high order central difference
- Large-eddy simulation
- Receptivity
- Shock sensor
Cite this
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High-order accurate large-eddy simulations of compressible viscous flow in cylindrical coordinates. / Karami, Shahram; Stegeman, Paul C.; Ooi, Andrew; Soria, J.
In: Computers and Fluids, Vol. 191, 104241, 15.09.2019.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - High-order accurate large-eddy simulations of compressible viscous flow in cylindrical coordinates
AU - Karami, Shahram
AU - Stegeman, Paul C.
AU - Ooi, Andrew
AU - Soria, J.
PY - 2019/9/15
Y1 - 2019/9/15
N2 - Dynamic interactions of shock waves and turbulent structures occur in a wide range of applications. The accurate simulation of turbulence in these flows requires a numerical scheme with minimal dissipation whereas the shock-capturing requires a dissipative scheme to stabilise the solution in the shock-wave discontinuous regions. These contradictory requirements make simulations of these flows extremely challenging. A compatible implementation of the solid boundary conditions at the point of incepting the acoustic waves and their internalisation into hydrodynamic instabilities is also challenging. Here we present, a high-fidelity, massively parallel and accurate solver for both direct numerical simulations and large-eddy simulations of supersonic turbulent flows in cylindrical coordinates. A hybrid WENO/ high order central difference scheme is used for the spatial discretisation with a fourth-order five-stage 2N-storage Runge–Kutta for the time integration. The least square contraction of Lilly [1] is utilised for large-eddy subgrid-scale modelling. The solid surface boundary condition is implemented using the offset wall and ghost cell technique. The numerical implementation is validated through a wide range of test cases from simple to more complex cases. The numerical results show good agreement with analytical solutions and available experimental results. In the large-eddy simulation of a supersonic under-expanded impinging jet, it is observed that the conventional Ducros sensor leads to a more dissipative hybrid scheme. In this paper, a new shock sensor based on a WENO smoothness indicator is proposed and it is demonstrated to perform better especially in the simulation of the supersonic under-expanded impinging jet by limiting the expensive WENO scheme to the discontinuous regions and reducing the computational cost by approximately 10%.
AB - Dynamic interactions of shock waves and turbulent structures occur in a wide range of applications. The accurate simulation of turbulence in these flows requires a numerical scheme with minimal dissipation whereas the shock-capturing requires a dissipative scheme to stabilise the solution in the shock-wave discontinuous regions. These contradictory requirements make simulations of these flows extremely challenging. A compatible implementation of the solid boundary conditions at the point of incepting the acoustic waves and their internalisation into hydrodynamic instabilities is also challenging. Here we present, a high-fidelity, massively parallel and accurate solver for both direct numerical simulations and large-eddy simulations of supersonic turbulent flows in cylindrical coordinates. A hybrid WENO/ high order central difference scheme is used for the spatial discretisation with a fourth-order five-stage 2N-storage Runge–Kutta for the time integration. The least square contraction of Lilly [1] is utilised for large-eddy subgrid-scale modelling. The solid surface boundary condition is implemented using the offset wall and ghost cell technique. The numerical implementation is validated through a wide range of test cases from simple to more complex cases. The numerical results show good agreement with analytical solutions and available experimental results. In the large-eddy simulation of a supersonic under-expanded impinging jet, it is observed that the conventional Ducros sensor leads to a more dissipative hybrid scheme. In this paper, a new shock sensor based on a WENO smoothness indicator is proposed and it is demonstrated to perform better especially in the simulation of the supersonic under-expanded impinging jet by limiting the expensive WENO scheme to the discontinuous regions and reducing the computational cost by approximately 10%.
KW - Cylindrical coordinate
KW - Hybrid WENO/ high order central difference
KW - Large-eddy simulation
KW - Receptivity
KW - Shock sensor
UR - http://www.scopus.com/inward/record.url?scp=85070223919&partnerID=8YFLogxK
U2 - 10.1016/j.compfluid.2019.104241
DO - 10.1016/j.compfluid.2019.104241
M3 - Article
VL - 191
JO - Computers and Fluids
JF - Computers and Fluids
SN - 0045-7930
M1 - 104241
ER -