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We propose an adaptive numerical solver for the study of viscoelastic 2Dtwo-phase flows using the volume-of-fluid method. The scheme uses the robustlog conformation tensor technique of Fattal & Kupferman (2004,2005} combinedwith the time-split scheme proposed by Hao & Pan (2007}. The use of thistime-split scheme has been proven to increase the stability of the numericalcomputation of two-phase flows. We show that the adaptive computationaltechnique can be used to simulate viscoelastic flows efficiently. The solver iscoded using the open-source libraries provided by the \basilisk \cite{Basilisk}platform. In particular, the method is implemented for Oldroyd-B typeviscoelastic fluids and related models (FENE-P and FENE-CR). The numericalscheme is then used to study the splashing of weakly viscoelastic drops. Thesolvers and tests of this work are freely available on the Basilisk web site

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of slightly viscoelastic droplets