Linear and quadratic invariants preserving discretization of Euler equations

In the context of the numerical treatment of convective terms in compressibletransport equations, general criteria for linear and quadratic invariants preservation, validon uniform and non-uniform (Cartesian) meshes, have been recently derived by using amatrix-vector approach, for both finite-difference and finite-volume methods ([1, 2]). Inthis work, which constitutes a follow-up investigation of the analysis presented in [1, 2],this theory is applied to the spatial discretization of convective terms for the system ofEuler equations. A classical formulation already presented in the literature is investigatedand reformulated within the matrix-vector approach. The relations among the discreteversions of the various terms in the Euler equations are analyzed and the additional degreesof freedom identified by the proposed theory are investigated. Numerical simulations ona classical test case are used to validate the theory and to assess the effectiveness of thevarious formulations.