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An improved algorithm for simulating three-dimensional, viscoelastic turbulence. (English) Zbl 1143.76349
Summary: We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by A. Kurganov and E. Tadmor [J. Comput. Phys. 160, No. 1, 241–282 (2000; Zbl 0987.65085)] that guarantees a scalar field remains everywhere positive. We have extended the algorithm to guarantee a tensor field remains everywhere positive definite following an update. Extensive testing of the algorithm shows that the volume average of the conformation tensor is conserved. Furthermore, volume averages of the conformation tensor in homogeneous turbulent shear flow made over the Eulerian grid are in quantitative agreement with Lagrangian averages made over fluid particles moving throughout the domain, highlighting the accuracy of the treatment of the convective terms.

MSC:
76-06 Proceedings, conferences, collections, etc. pertaining to fluid mechanics
76Mxx Basic methods in fluid mechanics
76Axx Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
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