Numerical scheme for simulation of transient flows of non-newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Acta Mechanica |
| Volume: | 230 |
| Number: | 3 |
| Year: | 2019 |
| Pages: | 729-747 |
| DOI: | 10.1007/s00707-019-2372-y |
| Abstract: | We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure–velocity–apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has—on the discrete level—a solution, and using the proposed scheme, we numerically solve several flow problems. |
| Preprint project: | NCMM |
| Preprint year: | 2019 |
| Preprint number: | 04 |
| Preprint ID: | NCMM/2019/04 |
| Keywords: | Couette flow, implicit constitutive relations, numerical simulation |
| Authors | |
| Added by: | [VP] |
| Total mark: | 0 |
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