Numerical simulation with low artificial dissipation of transitional flow over a delta wing

A low-dissipation simulation method is used to perform simulations of transitional aerodynamic flow over a delta wing. For an accurate simulation of such a flow, numerical conservation of important physical quantities is desirable. In particular, the discretization of the convective terms of the Navier-Stokes equations should not spuriously generate or dissipate kinetic energy, because this can interfere with the transition to turbulent flow. Conservation of discrete kinetic energy by the discretized convective terms can be achieved by writing the Navier--Stokes equations in square-root variables, which results in a skew-symmetric convective term. In the paper, simulations with such a low-dissipation method are presented at chord Reynolds numbers around 200,000. The results show good agreement with experimental measurements

Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow

The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions are sought for the local and global conservation of primary (mass and momentum) and secondary (kinetic energy) invariants on Cartesian meshes. The analysis, based on a matrix approach, shows that sharp criteria for global and local conservation can be obtained and that in many cases these two concepts are equivalent. Explicit numerical fluxes are derived in all finite-difference formulations for which global conservation is guaranteed, even for non-uniform Cartesian meshes. The treatment reveals also an intimate relation between conservative finite-difference formulations and cell-centered finite-volume type approaches. This analogy suggests the design of wider classes of finite-difference discretizations locally preserving primary and secondary invariants