• An efficient, entropy-stable high-order method for multicomponent flows is presented • The spatial residual is built via L 2 -projection of conservative to entropy variables. • The Direct Enforcement of Entropy Balance term is included to avoid over-integration • Performance is compared with other approaches in one-dimensional cases of increasing complexity • The entropy projection solver combines computational efficiency and entropy conservation/stability This paper presents the development of an efficient discontinuous Galerkin (dG) solver for the multicomponent compressible Euler equations. The method provides global entropy conservation/stability at the discrete level, contributing to the robustness of the computations, cf. 4, 19. The unsteady term of the governing equations is formulated for the conservative variables, while the spatial discretization is assembled from the L 2 -projection of the entropy variables 4 , 19 onto the dG function space, as suggested by Chan et al. 44 and Alberti et al. 35. This approach requires numerical over-integration to ensure entropy conservation/stability, significantly degrading the computational performance. The Direct Enforcement of Entropy Balance (DEEB) proposed by Abgrall in 11 is implemented to avoid this. The DEEB consists of an explicit correction to the discretization to avoid unphysical entropy evolution. As high-order discretizations give rise to spurious oscillations at flow discontinuities, a directional shock-capturing term is added to the discretized equations. The performance of the solver is compared to alternative approaches, i.e. , solving directly for the conservative or the entropy variables, by computing several one-dimensional cases. The convergence of the numerical solution is also tested using the method of manufactured solutions (MMS). The interactions of a shock wave with a circular and a square inhomogeneity are finally considered, assessing the accuracy of the solver for reproducing complex two-dimensional phenomena.
Roig et al. (Sun,) studied this question.