Boundaryfitted

Boundaryfitted refers to coordinate systems or grids that conform to the boundaries of a physical domain. In numerical simulation, boundaryfitted grids map a complex, possibly curved boundary in physical space to a simpler computational space, typically a rectangle or box, allowing accurate boundary condition specification and improved resolution near walls or interfaces.

The technique is common in finite difference and finite element methods. It uses curvilinear coordinates (xi, eta, zeta) such that x = X(xi, eta, zeta) and y = Y(xi, eta, zeta) (and z in three dimensions). The Jacobian of the transformation enters the governing equations, producing metric coefficients that adjust derivatives. Grid generation methods include elliptic grid generation, which solves Laplace-type equations to smooth grid lines, and algebraic approaches that place points directly to meet geometric constraints. Boundaryfitted grids can be static or dynamic, adapting as domains deform.

Applications span computational fluid dynamics, heat and mass transfer, electromagnetics, groundwater flow, and structural analysis, particularly for domains with curved boundaries such as airfoils, pipes, or biological geometries.

Advantages include faithful boundary representation, easier imposition of Dirichlet and Neumann conditions, and improved accuracy near boundaries. Challenges involve grid distortion with large deformations, coordinate singularities at corners or sharp curvature, the complexity of metric terms, and higher computational cost for grid generation and Jacobian evaluation.

Related concepts include body-fitted grids, curvilinear coordinates, and mesh generation techniques used to create boundaryfitted representations of complex geometries.