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High-order accurate large-eddy simulations of compressible viscous flow in cylindrical coordinates. (English) Zbl 1519.76211

Summary: 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 D. K. Lilly [“A proposed modification of the Germano subgrid-scale closure method”, Phys. Fluids, A 4, No. 3, 633–635 (1992; doi:10.1063/1.858280)] 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%.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
76F65 Direct numerical and large eddy simulation of turbulence
76N99 Compressible fluids and gas dynamics
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