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Velocity potential computation by finite differences for compressible flow in ducts
Author(s) -
O'Carroll M. J.
Publication year - 1975
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620090310
Subject(s) - discretization , mathematics , mathematical analysis , boundary value problem , hyperbola , computation , finite difference , compressibility , compressible flow , velocity potential , newton's method , nonlinear system , geometry , physics , mechanics , algorithm , quantum mechanics
Preliminary studies of computation with velocity potential are made with a view to the analysis of complex three‐dimensional flows. The methods used are applicable more generally to quasilinear elliptic problems with derivative boundary conditions on irregular domains. Second order finite difference approximations are constructed in simple form for plane ducts of general shape by using an irregular net. Derivative boundary conditions are handled quite easily. An iterative method is described which corresponds to freezing the coefficients in the quasilinear differential equation for velocity potential. The discretization is such that this is a ‘generalized Newton’ method for the non‐linear algebraic equations. Good convergence has been found in practice even when there are small supersonic zones. The discretization accuracy is tested by comparisons with the exact solution for incompressible flow between confocal hyperbolas.