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Pseudospectral method for transient viscoelastic flow in an axisymmetric channel. (English) Zbl 0781.76069
Summary: A new pseudospectral method for simulating transient viscoelastic flows is presented. The governing equations are a system of seven first-order equations of mixed type. The essential features of the method are (i) all seven independent flow variables are represented on a common Chebyshev- Gauss-Lobatto grid; (ii) the pressure is treated in such a way as to give a globally divergence-free velocity field, i.e., the divergence of the velocity field vanishes globally within the region, and (iii) different time scales pertaining within the hyperbolic constitutive equations are treated using the splitting technique of R. J. Le Veque and H. C. Yee [J. Comput. Phys. 86, No. 1, 187-210 (1990; Zbl 0682.76053)] originally proposed in a finite-difference context. The method is applied to transient axisymmetric flow of an Oldroyd B fluid in a channel formulated in two ways: (I) as an initial-boundary value problem, and (II) as a body-force problem.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76A10 Viscoelastic fluids
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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