Stability issues in time-domain methods for unstructured block meshing using local time-steps

International audienceTo find a stable Time-Domain (TD) numerical scheme, that adopts a local time-step in unstructured meshing, is a real challenge in numerical methods. This article presents a theoretical investigation on the origins of such instabilities. New finding shows that using multiple time-steps in one computational domain with TD methods produces a systematic error that does not tend to zero as both the spatial and temporal steps go to zero. This mathematical formulation leads to a new approach to elaborate stable TD algorithms that use local timestep. Eventually, some correction terms are introduced into update equations for all cells adjacent to boundaries that separate different blocks with different time-steps