An improvement of flow front computation through Bézier shape deformation guaranteeing mass conservation law

Abstract

This paper aims to define the flow front as a continuous curve, in particular a Bézier curve, to reduce the inaccuracies generated by classical Finite Elements (FEM) in the flow front definition. The flow front is used in LCM processes for optimization algorithms, on-line control systems, PPI index and in general for whatever design and correction task. In these algorithms it is commonly used FEM simulation where the flow front is represented as a set of discrete points. This fact introduces an inaccuracy with the real flow front, because is continuous. In addition, the shape of the flow front obtained by FEM simulation differs in a great manner from the smooth shape of the real flow front. This concept was solved in our previous research, [7], where, using a mathematical technique, a Bézier curve is deformed and moved using velocity vectors. This technique is called Bézier Shape Deformation. This work improved the flow front representation but also introduced inaccuracies. In particular, the area enclosed between two Bézier curves, the flow front in different time instants, do not corresponds to the resins amount introduced in this range of time. To solve it, in the present research it is guaranteed the mass conservation law. Hence, it is introduced the required enclosed area in the mathematical technique to guarantee that not only velocity vectors has an influence in the Bézier curve deformation.