Adaptive Coupled ALE Finite Element And Meshfree Method For Non-Isothermal Non-Newtonian Viscous Flow In Mould Filling Process

Injection molding is one of the most important industrial processes for the manufacturingof plastic products. Examples of such products are cassette tape boxes, computer keyboardsand so on. In the production process, molten polymer is injected with high velocity into anempty mold. Once the cavity is filled up and the polymer material is sufficiently solidified,the mold opens momentarily to eject the plastic component and the cycle repeats.Due to the constant demand for developing efficient analysis tools to replace the costlyand time-consuming experimental trial-and-error approach, numerical simulation of injectionmolding process has attracted increasing interest over the past years. However, there are stillmany aspects that require further research. For example, the free surface tracking and thenumerical solution for initial and boundary value problems of the governing equations withacceptable levels of overall performance in stability, efficiency, accuracy and robustness arestill open subjects. The present thesis is an effort towards these objectives.Accurately tracking the moving free surface plays an important role in the simulation ofinjection molding process. At present, the available strategies to tackle this problem can bemainly classified into Lagrangian, Eulerian and Arbitrary Lagrangian-Eulerian(ALE)methods depending on the configurations to which continuum mechanics formulations arereferred. Owing to the superiority of the ALE method which combines the respectiveadvantages of both Lagrangian and Eulerian methods by means of defining the mesh motionindependent of the material motion, a free surface tracking and mesh generation model basedon the ALE method is presented in Chapter 3 which can accurately determine locations ofadvancing free surfaces and meanwhile to minimize the distortion of the computational mesh.In this model, the real-time mesh generation of the domain with variable mass of the filledpolymer melts is simplified as a polygon's triangulation in the filled zone near the movingfront, that saves CPU time significantly. In addition, a local Laplacian smoothing technique isintroduced to improve the mesh quality and several strategies are proposed to cope with thecontact problems between the moving free surfaces and the boundaries of the mold cavity.Another critical ingredient to achieve the simulation is the robust numerical solutionscheme for initial and boundary value problems of the governing equations. It is well knownthat numerical modeling of incompressible flows with the classical Galerkin method maysuffer from numerical instabilities due to two main sources. The first attributes to the mixedcharacter of the governing equations which restricts the choice of interpolation spaces for thevelocity and pressure (u-p) fields. The incompatible interpolations, for example, the equallow order u-p interpolations, that violate the LBB condition may induce spurious spatialoscillations in the resulting pressure field. The second is associated with the convective character of the equations which induces oscillations particularly in the convection dominatedcases, as the standard Galerkin method is only valid for self-adjoint operator equations.As for the first problem, the contribution of the present thesis is that a Pressure StabilizedFractional Step Algorithm (PS-FSA) is developed which can effectively remove the spuriouspressure oscillations and has better pressure stability than that of the Classical Fractional StepAlgorithm (C-FSA). The proposed PS-FSA is based on re-writing the mass balance equationin the framework of the Finite Increment Calculus (FIC) theory and introducing an additionalvariable into the algorithm in a logical way to avoid the calculation of high order spatialderivatives. In addition, such pressure stabilization mechanism is also extended to theclassical Characteristic Based Split (CBS) algorithm to enhance its pressure stability. Thedetailed derivation of PS-FSA and its numerical validations are presented in Chapter 4.As for the second problem, the contribution of the present thesis is that a generalizedversion of the Characteristic Galerkin (CG) method in ALE framework is developed whichcan effectively cope with the convection dominated problem and can use larger time step sizethan that of the classical CG method. In fact, the classical CG and the classicalCrank-Nicolson (CN) methods can be classified as two special cases of this generalized CGmethod respectively. In addition, the generation is also exhibited by the fact that the ALEdescription employed for the derivation of the proposed method can reduce to the Euleriandescription used in the classical CG method if the reference coordinates are fixed in space.Due to this generation, it is convenient to combine the proposed CG method with the ALEfree surface tracking techniques mentioned above. By combining the proposed generalizedCG method with the fractional step algorithm and the pressure stabilization techniquedeveloped in Chapter 4, an iterative pressure-stabilized generalized CBS algorithm is formedand used for non-isothermal non-Newtonian fluid flows. The detailed derivation of thealgorithm and its numerical validations are presented in Chapter 6.Another important contribution of the present thesis is that a self-adaptive domainpartition algorithm is proposed which can automatically partition the whole computationaldomain into three sub-domains where the finite element (FE), meshfree (MF) and theircoupled approximations are employed respectively. Based on this adaptive procedure and theContinuous Blending Method (CBM), an adaptive coupled FE and MF method is alsoproposed for the simulation of injection molding process, which can adequately exploit therespective strong points of FE and MF methods and meanwhile avoid their respective weakpoints. The details of this method and the numerical results to demonstrate its superiority overthe independent FE and MF methods are presented in Chapter 5.For the purpose of self-completeness, the fundamental concepts and issues of themeshfree method with Galerkin weak form are summarized in Chapter 2. The computer program and data structures to implement the algorithms presented in this thesis for thenumerical simulation of injection molding process are provided in Chapter 7. Conclusion andfuture developments are given in Chapter 8.