Transfinite Interpolation of Surfaces with Integral Constraints Using a Design Language

We discuss the problem of geometric design of curved ducts with variable crosssection by transfinite interpolation with integro-differential constraints. This work is a contribution to a research program including numerical simulation and preliminary design of an experimental apparatus for studying fluid-dynamics of air in internal combustion engines of new conception. The proposed geometric modeling approach is based on piecewise multivariate transfinite interpolation of assigned cross-sections, via combination of section-generating functions with univariate quintic Hermite's polynomials. The volume mapping produced by such transfinite interpolation is composed with a local section scaling extracted from a one-parameter family of affine transformations, where the diagonal coefficients depend on the ratio between the areas of the starting and current sections. An approriately chosen point sampling of the duct generated by the composition of volume mapping and section scaling is employed to generate a cell decomposition of the duct volume with tetrahedral elements. Such elements are used for numerical simulation of the fluid-dynamics problem.