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Partially Implicit BDF2 Blends for Convection Dominated Flows

In this paper we consider various blends of implicit and explicit time integration schemes based on the well-known BDF2 method, applied to convection-diffusion problems with dominating convection. A fully implicit treatment of convection terms is often not very efficient. We shall deal with schemes that are implicit in the convection terms only locally in space, without introducing the internal inconsistencies that are common with many time-splitting methods. Along with implementation aspects of the implicit relations, we shall discuss accuracy of the schemes, positivity and monotonicity properties.