Flow numerical computation through Bezier shape deformation for LCM process simulation methods

The flow front advance computation is commonly used in Liquid Composite Molding simulation for design optimization algorithms, quality process performance, etc. It can be used also to take corrective decisions in on-line control systems for the flow redirection during filling. In these cases, the flow front can be composed by a large number of nodes. In particular, it can be computed by thousands of nodes using a CCD as Finite Element sensor with high resolution [1]. Therefore, a methodology to reduce it in a few significant points is required to improve the computational costs of whatever algorithm that uses the flow front behavior information. In other previous research results, a new mathematical formulation of the flow front using CAGD techniques was used [1], [2]. Therefore, the flow front is formulae in a Bezier curve permitting to represent whatever flow front shape in a few representative points. In particular the common flow front shapes can be represented in just 10 points. The flow front nodes were approximated in a Bezier curve using a least square method to estimate the control points of the Bezier curve and a projection of this into itself. In CAGD fields, there are another interesting techniques that can be used for this propose. In particular, there is an interesting topic known as “Bezier shape deformation” [3]. This topic treats the deformation of a predefined Bezier curve through vectors. Hence, whatever point of the Bezier curve can be moved using the modulus and the direction of this vector. Therefore, the velocity vector field obtained solving the flow kinematics with Finite Element Method (FEM) or Natural Element Method (NEM) can be used to deform a predefined Bezier curve. This flow front parameterization permits a continuous numerical formulation of the flow front avoiding the approximation techniques used in [1], [2]. This computation was also extended to study particle tracking during filling.