Renardy, Michael; Renardy, Yuriko On the nature of boundary conditions for flows with moving free surfaces. (English) Zbl 0739.76016 J. Comput. Phys. 93, No. 1, 325-335 (1991). The authors have considered small perturbations of plane parallel flow between a wall and a moving free surface. The problem is posed on a rectangle with inflow and outflow boundaries. The usual boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. Nature of boundary conditions, which can be imposed at the inflow and outflow boundaries in order to yield a well-posed problem are examined. Numerical simulations with the FIDAP package are used to illustrate the analytical results. Reviewer: J.Prakash (Bombay) Cited in 3 Documents MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 76E05 Parallel shear flows in hydrodynamic stability 35R35 Free boundary problems for PDEs Keywords:small perturbations; plane parallel flow; moving free surface; inflow boundaries; outflow boundaries; FIDAP package Software:FIDAP PDFBibTeX XMLCite \textit{M. Renardy} and \textit{Y. Renardy}, J. Comput. Phys. 93, No. 1, 325--335 (1991; Zbl 0739.76016) Full Text: DOI References: [1] Engelman, M. S.; Sani, R. I.: C.taylorj.a.johnsonw.r.smith computational techniques for fluid flow. Computational techniques for fluid flow, 47 (1986) · Zbl 0623.76016 [2] Solonnikov, V. A.: H.brézisj.l.lions nonlinear partial differential equations and their applications, college de France seminar. Nonlinear partial differential equations and their applications, college de France seminar, 340 (1982) [3] Jean, M.: Arch. rational mech. Anal.. 74, 197 (1980) [4] Lions, J. L.; Magenes, E.: Non-homogeneous boundary value problems and applications. 1 (1972) · Zbl 0223.35039 [5] Renardy, M.: Corner singularities between free surfaces and open boundaries. Z. angew. Math. phys. 41, 419 (1990) · Zbl 0706.76030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.