An implicit cell-centered Lagrange-Remap scheme for all speed flows

• A second-order time-accurate implicit Lagrange-Remap (LR) scheme is proposed.
• The numerical flux is given by the acoustic Riemann solver.
• The acoustic Riemann solver is modified for low Mach number as well as supersonic flows.
• The Lagrange step solves implicitly the hyperbolic equations of pressure and velocities.
• The new LR scheme maintains all conservative quantities, and is general for any EOS.

A second-order time-accurate implicit scheme is constructed for the Lagrange-Remap (LR) strategy. The numerical flux is given by the simple acoustic Riemann solver. The Riemann solver is modified by introducing a scaling coefficient so that the scheme can deal with very subsonic (low Mach) flows as well as supersonic flows. The Lagrange step solves implicitly the hyperbolic equations of pressure and velocities under the isentropic assumption by the trapezoidal time integration method. The new LR scheme maintains exactly the conservation of mass, momentum and energy, and it is general for materials with any equation of state. Numerical tests show that the LR scheme using the simple but general Riemann solver can resolve shock waves sharply for supersonic flows, and resolve well the acoustic waves in low Mach number flows as low as M = 0.001.