An improvement of convection fidelity in Euler calculations

Elimination of spurious loss in Euler equation computations

“…Spurious losses are thus eliminated, allowing acceptable solutions on extremely coarse grids. Other loss-mitigation techniques have been presented by Lee and Chu [2] who employ a Clebsch velocity decomposition, and by Denton and Xu [3] who employ the entropy conservation equation with an ad-hoc source term at shocks.…”

“…(1) (2) (3) (4) The velocity vector q and its magnitude q are defined in terms of the cartesian velocity components, dt where + V -(pqS) = 0 (5) S = In (^ ^ } (6) which shows that the entropy 5 should be constant throughout the flow if it is constant at the upstream boundary. In practice, however, the discrete forms of equations (1,2,3,4) must be stabilized with dissipative terms, which either appear naturally as truncation errors or are added explicitly, depending on the discretization scheme used.…”