Local time stepping for a mass‐consistent and time‐split advection scheme

An advection scheme that is locally mass‐conserving, positive‐definite, and has strongly reduced splitting errors in deformational flows is presented in a recent work by Bott. Additionally, a row‐oriented substepping is proposed to deal with Courant numbers C larger than one. However, this leads to either a nonlocal communication pattern or a violation of numerical reproducibility under domain decomposition in a (massively) parallel computing environment. Instead, a local time stepping is proposed here, which acts only on those grid points where C exceeds one. It is shown that this local time stepping maintains the above‐mentioned properties of the Bott scheme and that it achieves numerical reproducibility, together with a slight improvement in efficiency.