High order time integration and mesh adaptation with error control for incompressible Navier–Stokes and scalar transport resolution on dual grids

Relying on a building block developed by the authors in order to resolve the incompressible Navier–Stokes equation with high order implicit time stepping and dynamic mesh adaptation based on multiresolution analysis with collocated variables, the present contribution investigates the ability to extend such a strategy for scalar transport at relatively large Schmidt numbers using a finer level of refinement compared to the resolution of the hydrodynamic variables, while preserving space adaptation with error control. This building block is a key part of a strategy to construct a low-Mach number code based on a splitting strategy for combustion applications, where several spatial scales are into play. The computational efficiency and accuracy of the proposed strategy is assessed on a well-chosen three-vortex simulation.