Modeling parametric solids based on arbitrary framework and non-uniform linear interpolation

This article describes a method for constructing a parametric solid based on a framework consisting of a set of curved hexagonal portions whose opposite boundaries of non-rectangular quadrilateral faces have different parametric lengths. Parametric solids can model both the shape and anisotropic interior based on a given framework without transforming it or duplicating its information. Equations for body portions of types r₀, r₁, and r₂ are presented, constructed using non-uniform linear interpolation, to determine initial or boundary conditions in numerical simulations. A three-dimensional computational mesh with variable cell size is created by dividing the body portion into elements whose size is determined by local requirements. This approach, in demand in computational aerodynamics, heat and mass transfer, and other engineering calculations, enables greater accuracy in areas where parameters change rapidly, while simultaneously optimizing the use of computational resources by using larger cells in areas with smooth changes. The wellknown Coons portion equation for a unit cube is a special case of the obtained equations.

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