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Multigrid solution of compressible turbulent flow on unstructured meshes using a two‐equation model
Author(s) -
Mavriplis D. J.,
Martinelli L.
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.1650181002
Subject(s) - multigrid method , turbulence , reynolds averaged navier–stokes equations , mathematics , polygon mesh , euler equations , navier–stokes equations , compressible flow , flow (mathematics) , aerodynamics , k epsilon turbulence model , turbulence modeling , compressibility , mathematical analysis , partial differential equation , mechanics , physics , geometry
Abstract The steady state solution of the system of equations consisting of the full Navier‐Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge‐Kutta time‐stepping scheme with a stability‐bound local time step, while the turbulence equations are advanced in a point‐implicit scheme with a time step which guarantees stability and positivity. Low‐Reynolds‐number modifications to the original two‐equation model are incorporated in a manner which results in well‐behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.