High-order staggered schemes for compressible hydrodynamics. Weak consistency and numerical validation.

Highlights • High-order accuracy in space is done via Taylor series, whereas in time it is reached through Runge–Kutta methods. • Weak consistency of staggered schemes is proved for barotropic hydrodynamics. • Weak consistency is proved for compressible hydrodynamics using an a posteriori internal energy corrector. • Wide variety of numerical test-cases illustrate the interest, the robustness and the convergence of the schemes. Abstract Staggered grids schemes, formulated in internal energy, are commonly used for CFD applications in industrial context. Here, we prove the consistency of a class of high-order Lagrange-Remap staggered schemes for solving the Euler equations in 1D and 2D on Cartesian grids. The main result of the paper is that using an a posteriori internal energy corrector, the Lagrangian schemes are proved to be conservative in mass, momentum and total energy and to be weakly consistent with the 1D Lagrangian formulation of the Euler equations. Extension in 2D is done using directional splitting methods and face-staggering. Numerical examples in both 1D and 2D illustrate the accuracy, the convergence and the robustness of the schemes. [ABSTRACT FROM AUTHOR]