A convergence analysis of the affine particle-in-cell method and its application in the simulation of extrusion processes
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Simulation of extrusion processes represents a large challenge for commonly used numerical methods. In our application for example, a hot melt is extruded whilst being rapidly cooled. Under these conditions of quenching, spinodal phase separation occurs which causes the formation of a characteristic micro-structure of the extrudate, consisting of solid and liquid phases. We model this process using a variant of the Material Point Method (MPM) , namely the Aﬃne Particle-In-Cell (APIC) method . Its hybrid particle/grid character is advantageous for simulating both ﬂuid and solid behavior: pure Eulerian particle methods, such as classic SPH, fail for simulating solids, particularly in tension, whereas pure Lagrangian methods generally cannot cope with large deformations caused by material ﬂow. APIC improves upon the original MPM method by using a so-called locally aﬃne velocity representation  which allows the conservation of linear and angular momentum without the need of potentially unstable Fluid-Implicit-Particle (FLIP) techniques . We analyze the convergence behavior of APIC and compare its accuracy against a traditional MPM variant, the Generalized Interpolation Material Point Method (GIMP).
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