Multistage explicit advective prediction for projection-type incompressible flow solvers

A multistep advective predictor has been developed within the context of projection schemes for incompressible flows. The key idea is to integrate with schemes of different order the different regions of the domain. In regions where advection dominates, multistepping yields a considerable benefit. In those regions where viscosity dominates, the scheme reverts naturally to the original one-step scheme. Several examples show savings of the order of 1:3–1:10 as compared with standard projection schemes, even for transient problems. Given that these benefits can be achieved with a very modest change in existing codes, the proposed multistage advective predictor should be widely applicable.