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Pressure jump conditions for Stokes equations with discontinuous viscosity in 2D and 3D. (English) Zbl 1142.76022
Summary: The jump conditions for normal derivative of pressure have been derived for two-phase Stokes (and Navier-Stokes) equations with discontinuous viscosity and singular sources in two and three dimensions. While different jump conditions for the pressure and velocity can be found in the literature, the jump condition for the normal derivative of pressure is new. The derivation is based on the immersed interface method that uses a fixed local coordinate system and the balance of forces along the interface that separates two phases. The derivation also provides a way to compute the jump conditions. The jump conditions for pressure and velocity are useful in developing accurate numerical methods for two-phase Stokes and Navier-Stokes equations.

76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI Euclid