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A new mesh-based coupling method for multi-physics applications, such as fluid-structure interaction, has been implemented in the B2000++ system: The Common Refinement Mesh and L2 minimization (see X Jiao, M. T. Heath, Common-refinement-based data transfer between non-matching meshes in multiphysics simulations, Int. J. Numer. Meth. Engng. 2004; 61).
The method allows for coupling of two polynomial surface fields from similar but non-matching meshes, such as displacements and pressures/tractions in aeroelastic coupling. It is based on the minimization of the difference of field quantities, such as surface pressure and surface displacement fields between the coupled surfaces or lines with L2 norm. While it requires accurate integration over the surfaces, i gives very accurate results, and it guarantees conservation of quantities.
In B2000++ the coupling method is implemented as a boundary condition, adding extra degrees of freedom to the system and solving for the interpolated field values in the current solution step, i.e. the system of non-linear constraint equations is solved together with the B2000++ solver with the augmented Lagrange multiplier method.
The method is illustrated schematically with a 2D aeroelastic coupling problem, leading to a 1D interpolation problem along the common surface or line:
