Implicit linearity preservation type schemes for moving meshes

We are concerned with the accurate implicit approximation of compressible flows in a fixed and moving mesh context, such as piston engine flows. Geometries are commonly complex and flows compressible. Therefore, it is convenient to develop the numerical approach in the context of a space-time finite-volume formulation for unstructured meshes. The hyperbolic flux is obtained by a generalized Riemann solver taking into account the mesh motion. Using the linearity preservation property we propose a new class of stable implicit schemes developing low numerical viscosity. These schemes can be viewed as a correction of the usual MUSCL flux, induced by the time derivative and mesh motion. Accurate numerical results are obtained for transonic (shock tube) as well as low Mach number flows (diesel engine). It is numerically proved, that for large time steps, those approximations can be as accurate as some explicit schemes. The proposed schemes, due the compactness of the stencils, are well adapted for parallelization strategy.