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# Chapter 4: Numerical Implementation for the Filling and Packing Simulation

Huamin Zhou, Zixiang Hu, Yun Zhang, and Dequn Li

State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, Hubei, China

In the previous chapter, we have got the governing equations in the filling and packing phases. In this chapter, we first introduce some common numerical methods for the mathematical problems to be solved. Then, some methods for tracking moving melt front are presented as an essential problem in the filling simulation of the injection mold. Finally, some methods for solving algebraic equations are discussed; meanwhile, parallel algorithms are also mentioned.

# 4.1 Numerical Methods

The filling and packing computer simulation of injection molding is mainly involved with the application of computational fluid dynamics (CFD) and numerical heat transfer (NHT). Often, a model that represents a polymer process is in the form of an algebraic equation, a set of nonlinear partial differential equations (PDEs) and/or an integral equation, which do not have analytical solutions. Numerical analysis will provide methods for obtaining useful solutions to those mathematical problems. Such methods will give an approximate but satisfactory solution to the problem, which can be used to interpret and understand the problem. In the past decades, thanks to the evolution of the high speed digital computers, numerical simulation has evolved together ...

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