“…Steady Euler equations play an important role in aerodynamic shape optimization problems [1,14], and have been viewed as a benchmark problem to evaluate the performance of various numerical schemes in computational fluid dynamics (CFD), see [4,24,37,44,45] among others. A lot of numerical methods have been developed to solve the unsteady and steady Euler equations, e.g., the discontinuous Galerkin method [4,33,50,51], the finite volume method [3,22,36,44], the spectral volume method [47], and the fast sweeping method [11,12].…”