An entropy fixed cell‐centered Lagrangian scheme

On the basis of the work P.‐H. Maire, R. Abgrall, J. Breil, J. Ovadia, SIAM J. Sci. Comput. 29 (2007), 1781–1824], we present an entropy fixed cell‐centered Lagrangian scheme for solving the Euler equations of compressible gas dynamics. The scheme uses the fully Lagrangian form of the gas dynamics equations, in which the primary variables are cell‐centered. And using the nodal solver, we obtain the nodal viscous‐velocity, viscous‐pressures, antidissipation velocity, and antidissipation pressures of each node. The final nodal velocity is computed as a weighted sum of viscous‐velocity and antidissipation velocity, so do nodal pressures, whereas these weights are calculated through the total entropy conservation for isentropic flows. Consequently, the constructed scheme is conservative in mass, momentum, and energy; preserves entropy for isentropic flows, and satisfies a local entropy inequality for nonisentropic flows. One‐ and two‐dimensional numerical examples are presented to demonstrate theoretical analysis and performance of the scheme in terms of accuracy and robustness.Copyright © 2013 John Wiley & Sons, Ltd.