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Solution of the compressible flow equations
Author(s) -
Gelder D.
Publication year - 1971
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.1620030107
Subject(s) - mathematics , discretization , compressible flow , mach number , flow (mathematics) , convergence (economics) , monotonic function , finite element method , mathematical analysis , compressibility , function (biology) , square (algebra) , geometry , physics , mechanics , thermodynamics , evolutionary biology , biology , economics , economic growth
A technique is described for solving the compressible flow equations in subsonic flow. The general quasi‐linear equation ∇. g ∇ v = 0 is considered with g a function of ∇ v . ∇ v , and iterations of the form ∇. g n ∇ v n + 1 = 0 are analysed, where g 0 is suitably chosen and g n defined from v n for n ≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution. Reliable convergence has been obtained in practice solving the linear equation for ø n +1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the finite element method.