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A Newton's method scheme for solving free‐surface flow problems
Author(s) -
Dandy David S.,
Leal L. Gary
Publication year - 1989
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650091204
Subject(s) - inviscid flow , mathematics , newton's method , convergence (economics) , algebraic equation , compressibility , flow (mathematics) , quadratic equation , mathematical analysis , classical mechanics , geometry , nonlinear system , mechanics , physics , quantum mechanics , economics , economic growth
Abstract A Newton's method scheme is described for solving the system of non‐linear algebraic equations arising when finite difference approximations are applied to the Navier–Stokes equations and their associated boundary conditions. The problem studied here is the steady, buoyancy‐driven motion of a deformable bubble, assumed to consist of an inviscid, incompressible gas. The linear Newton system is solved using both direct and iterative equation solvers. The numerical results are in excellent agreement with previous work, and the method achieves quadratic convergence.