A CFD/CSD interaction methodology for aircraft wings Page: 4 of 37
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Coupled approaches for solving aeroelastic problems are usually categorized in two ways:
loosely or strongly coupled. The loosely coupled approaches can be integrated or modular.
Integrated. loosely coupled methods alter the source code of either the CSD or CFD analysis
tool by including the coupling schemes in either code. Though the codes are integrated,
the CFD and CSD equations are not being altered and are solved independently. Modular,
loosely coupled methods do not integrate the coupling schemes into either the CFD or CSD
code. This allows the use of a variety of CFD/CSD codes.
Strongly or fully (single domain) coupled approaches require the solution of the CFD and
CSD equations simultaneously which necessitates the reformulation of the equations of each
discipline.8 The numerical matrices associated with the structures are orders of magnitude
stiffer than those associated with fluids. Thus, it is numerically inefficient or even impossible
to solve both systems using a monolithic numerical scheme.7 Recently, there have been
renewed attempts to solve both fluids and structures in a single computational domain.9" 0
However, they have been limited to simple two-dimensional problems and have not proven
to be better than the loosely coupled approach.
Guruswamy and Yang6 demonstrated a loosely coupled approach to aeroelasticity. The
fluids and structures were modeled independently and exchanged boundary information to
obtain aeroelastic solutions. The fluids were modeled using finite-difference based transonic
small disturbance (TSD) equations. The structures were modeled using finite element equa-
tions. The two disciplines were coupled to solve aeroelastic problems of two-dimensional
airfoils. This loosely coupled or domain decomposition approach was shown to be efficient
and accurate. This approach has been extended to three-dimensional problems and is in-
corporated into advanced aeroelastic codes as XTRAN3S," ATRAN3S,'2 and CAP-TSD.13
Guruswamy'4"5 also demonstrated the same technique by modeling fluids with Euler/Navier-
Stokes equations on moving grids. Matching the CFD grid displacements with the CSD or
finite element model response maintains the accuracy of this loosely coupled approach.3
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Bhardwaj, M.K.; Kapania, R.K.; Reichenbach, E. & Guruswamy, G.P. A CFD/CSD interaction methodology for aircraft wings, report, January 1, 1998; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc702492/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.