Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates. (English) Zbl 1316.76064
Summary: We discuss stabilization strategies for finite-difference approximations of the compressible Euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables. Our approach rather relies on a skew-symmetric-like splitting of the convective derivatives, that guarantees preservation of kinetic energy in the semi-discrete, low-Mach-number limit. A locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers. The validity of the approach is tested for benchmark flow cases, including the propagation of a cylindrical vortex, and the head-on collision of two vortex dipoles. The tests support high accuracy and superior stability over conventional central discretization of the convective derivatives. The potential use for DNS/LES of turbulent compressible flows in complex geometries is discussed.
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 |
| 76N99 | Compressible fluids and gas dynamics |
Keywords:
finite difference schemes; compressible flows; energy conservation; split convective operators; generalized curvilinear coordinatesSoftware:
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