Optimization of DNS/LES explicit solvers for combustor simulations using local time-stepping

In the context of numerical simulation of combustion, large disparities of geometrical length scales are encountered in combus-tion chambers. Indeed, differences in mesh cell sizes between a small injector and the overall combustion chamber may present several orders of magnitude. When considering an explicit solver for fully compressible Navier-Stokes equations, the global time step is constrained through a CFL-like condition by the size of the smallest cells in the overall computational domain. Local refinement of the injector leads to an inhomogeneous mesh and the former restriction drastically alters the overall solver efficiency. Local time stepping (LTS) methods is a solution to address this issue. A new LTS method suited for parallel solvers is presented is this work. The domain is divided into subgrids composed of cells that have approximately the same size. Flow equations are simultaneously advanced on each subgrid that have a local time-step adapted to satisfy the local CFL condition. Promising results from tests carried out on the 1D advection equation are shown here, that demonstrate the stability and accuracy of the method through numerical evidence. Indeed, the method leads at worse to a slight loss of accuracy of the solution