Consistent Internal Energy Based Schemes for the Compressible Euler Equations

Theorem 4.1 (Unconditional stability of the scheme) Let us suppose that the discrete heat diffusion operator satisfies the monotonicity property (3.20), that the equation of

With this correction, we are once again able to prove, in 1D, the consistency of the scheme in the Lax-Wendroff sense; more precisely speaking, passing to the limit separately in

The internal energy balance features a corrective source term which is needed for the scheme to compute the correct shock solutions: we are indeed able to prove a Lax consistency

We finally obtain a class of schemes which offer many interesting properties: both the density and internal energy positivity are preserved, unconditionnally for the pressure

In our method, energy-preserving schemes are obtained as a discrete analogue of the Euler–Lagrange equation that is derived by using the symmetry of time translation of the

In the present paper, we apply a similar strategy for the porous medium equation and the system of isentropic Euler equations in one space dimension, and derive numerical methods

The proposed scheme is built in such a way that the assumptions of this stability result hold (Sect. 3.3); this implies first a prediction of the density, as a non- standard first step

The plan of this paper is the following: in Section 2, we define the closure laws to close the Euler system (1) for a gas mixture and a fluid mixture, we recall some important