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A numerical study of unsteady, thermal, glass fiber drawing processes. (English) Zbl 1079.35082

Summary: An efficient second-order stable numerical method is presented to solve the model partial differential equations of thermal glass fiber processing. The physical process and structure of the model equations are described first. The numerical issues are then clarified. The heart of our method is a MacCormack scheme with flux limiting. The numerical method is validated on a linearized isothermal model and by comparison with known exact stationary solutions. The numerical method is then generalized to solve the equations of motion of thermal glass fiber drawing, exhibiting order of convergence. Further, the nonlinear PDE scheme is benchmarked against an independent linearized stability analysis of boundary value solutions near the onset of instability, which demonstrates the efficiency of the method.

MSC:

35Q35 PDEs in connection with fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
74F05 Thermal effects in solid mechanics
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