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A systematic analysis of the discrete conservation properties ofnon-dissipative, central-difference approximations of the compressibleNavier-Stokes equations is reported. A general triple splitting of thenonlinear convective terms is considered, and energy-preserving formulationsare fully characterized by deriving a two-parameter family of split forms.Previously developed formulations reported in literature are shown to beparticular members of this family; novel splittings are introduced anddiscussed as well. Furthermore, the conservation properties yielded bydifferent choices for the energy equation (i.e. total and internal energy,entropy) are analyzed thoroughly. It is shown that additional preservedquantities can be obtained through a suitable adaptive selection of the splitform within the derived family. Local conservation of primary invariants, whichis a fundamental property to build high-fidelity shock-capturing methods, isalso discussed in the paper. Numerical tests performed for the Taylor-GreenVortex at zero viscosity fully confirm the theoretical findings, and show thata careful choice of both the splitting and the energy formulation can provideremarkably robust and accurate results.

Numerically stable formulations of convective terms for turbulent compressible flows