An implicit finite-difference method for solving the Navier-Stokes equation using orthogonal curvilinear coordinates

Abstract Orthogonal curvilinear mesh networks are generated numerically between the wavy walls of two-dimensional peristaltic channels. A dual iterative procedure is developed to facilitate the conformal mapping, as well as to adjust mesh dimensions when necessary to fit the boundaries of the flow region. An implicit finite-difference technique is employed to obtain transient solutions of the Navier-Stokes equations. The effects of initial conditions on the flow establishment are discussed, along with considerations of numerical accuracy. The effects of certain nonconservative difference forms of the governing equations are explored. A calculated velocity field for a two-dimensional nonlinear peristaltic flow is supported by laboratory flow observation. The present method is applicable for laminar flow in a nonuniform channel with or without wall peristalsis.

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