Newton's method solver for the axisymmetric Navier-Stokes equations

Abstract

A new two-dimensional Newton's method Navier-Stokes solver is extended to the axisymmetric form of the equations. Roe's flux difference splitting is applied to the axisymmetric equations using Glaister's approach. A geometric conservation law correction term is added to insure satisfaction of the uniform stream reproduction criteria. Higher-order accuracy is attained through the use of Spekreijse's interpolation procedure with Van Albada's contiouous limiter. Harten and Hyman's minimum eigenvalue correction is also included