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Generalized potential flow theory and direct calculation of velocities applied to the numerical solution of the Navier‐Stokes and the Boussinesq equations
Author(s) -
Zijl Wouter
Publication year - 1988
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.1650080507
Subject(s) - bernoulli's principle , mathematics , conservative vector field , scalar (mathematics) , mathematical analysis , flow (mathematics) , boussinesq approximation (buoyancy) , computational fluid dynamics , navier–stokes equations , generalization , fluid dynamics , classical mechanics , mechanics , physics , compressibility , geometry , natural convection , convection , rayleigh number , thermodynamics
A formulation based on three scalar functions or potentials is applied to analyse the Navier‐Stokes and Boussinesq equations in three dimensions. In this formulation an explicit expression for the pressure exists, the so‐called generalized Bernoulli equation. Therefore the scalar functions formulation may be considered as a generalization of the well‐known potential flow and Bernoulli theory for irrotational fluid motion. The many advantages of this formulation applied to three‐dimensional Navier‐Stokes and Boussinesq flow will be discussed, and a numerical example is given as an illustration.