Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows. (English) Zbl 1375.76113
Summary: The form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Y. Morinishi et al. [J. Comput. Phys. 143, No. 1, 90–124 (1998; Zbl 0932.76054)], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow. These forms are analytically equivalent if the continuity is satisfied, and the skew-symmetric form is secondary conservative without the aid of the continuity, while the divergence form is primary conservative. The relations between the present and existing quasi-skew-symmetric forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-symmetric form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow.
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 |
Keywords:
convective term; compressible flow; skew-symmetric form; divergence form; advective form; finite difference; compact finite difference; fully conservative; secondary conservative; staggered grid system; regular grid systemCitations:
Zbl 0932.76054References:
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