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Partially implicit BDF2 blends for convection-dominated flows. (English) Zbl 1007.76052
Author’s summary: 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 deal with second-order schemes that are implicit in convective terms only locally in space, without introducing internal inconsistencies that are common with many time splitting methods. Along with implementation aspects of implicit relations, we discuss the accuracy of schemes, positivity and monotonicity properties.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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