Premium
Finite element solution of the streamfunction‐vorticity equations for incompressible two‐dimensional flows
Author(s) -
Comini G.,
Manzan M.,
ino C.
Publication year - 1994
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.1650190605
Subject(s) - stream function , vorticity , mathematics , vorticity equation , finite element method , upwind scheme , incompressible flow , pressure correction method , two dimensional flow , navier–stokes equations , reynolds number , computational fluid dynamics , mathematical analysis , compressibility , flow (mathematics) , geometry , vortex , mechanics , physics , discretization , turbulence , thermodynamics
Abstract The streamfunction‐vorticity equations for incompressible two‐dimensional flows are uncoupled and solved in sequence by the finite element method. The vorticity at no‐slip boundaries is evaluated in the framework of the streamfunction equation. The resulting scheme achieves convergence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the approach are demonstrated by the solution of two well‐known benchmark problems: flow in a lid‐driven cavity at Re ⩽ 10,000 and flow over a backward‐facing step at Re = 800.