A composite adaptive grid generation and migration technique for materials processing problems

Abstract

Simulation of complex materials processing problems requires a multifaceted approach. It is composed of a robust adaptive grid generation scheme, particularly suitable for moving boundary problems, an associated generalized flow solver for flow and energy equations with special treatment for free and moving interfaces, and an efficient parallel algorithm that can exploit the latest developments in computing hardware and software. This paper presents a systematic approach to efficient numerical algorithms, which can significantly enhance the ability to analyze/simulate a wide variety of materials processes. A composite adaptive grid generation and migration (CAGGM) scheme that is especially suitable for irregular boundaries with free and moving interfaces has been developed. CAGGM is based on a multidomain approach to decomposing a two-dimensional or three-dimensional (2D or 3D) physical domain into a number of subdomains. The interface/free surface positions are better managed using high order bicubic interpolation techniques. The interpolation scheme employs 2D curve fitting (or 3D surface fitting) procedures for rectangular or scattered data points through local treatments, to achieve realistic functional behavior, and is based on the work of Akima [ACM Trans. Math. Software, 22 (1996), pp. 357-361; ACM Trans. Math. Software, 22 (1996), pp. 362-371] and other computational geometry algorithms like "Delaunay triangulation" by Renka [ACM Trans. Math. Software, 22 (1986), pp. 1-8]. A multiphase adaptive grid generation and migration (MAGGM) scheme has also been formulated and implemented to improve the grid and solution characteristics for changing area/volume of the subdomains through grid addition/deletion based on a number of solution criteria. It helps carry out dynamic simulations with proper grid density control.