Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme
| Autor: | Ilya Peshkov, Walter Boscheri, Michael Dumbser, Evgeniy Romenski, Simone Chiocchetti, Matteo Ioriatti |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Computer Science
Hyperbolic equations Staggered mesh Constitutive equation FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas NO Physics::Fluid Dynamics Viscosity 0103 physical sciences FOS: Mathematics Mathematics - Numerical Analysis Stress relaxation 0101 mathematics Yield stress Mathematics Partial differential equation Viscoplasticity Mathematical analysis General Engineering Fluid Dynamics (physics.flu-dyn) Semi-implicit scheme Physics - Fluid Dynamics Numerical Analysis (math.NA) Non-Newtonian fluid 010101 applied mathematics Nonlinear system Solid mechanics Relaxation (approximation) Viscoplastic fluids |
| Popis: | We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosity concept of the Navier-Stokes theory and representation of the solid state as an infinitely rigid non-deformable solid, the solid state in our theory is deformable and the fluid state is considered rather as a "melted" solid via a certain procedure of relaxation of tangential stresses similar to Maxwell's visco-elasticity theory. The model is formulated as a system of first-order hyperbolic partial differential equations with possibly stiff non-linear relaxation source terms. The computational strategy is based on a staggered semi-implicit scheme which can be applied in particular to low-Mach number flows as usually required for flows of non-Newtonian fluids. The applicability of the model and numerical scheme is demonstrated on a few standard benchmark test cases such as Couette, Hagen-Poiseuille, and lid-driven cavity flows. The numerical solution is compared with analytical or numerical solutions of the Navier-Stokes theory with the Herschel-Bulkley constitutive model for nonlinear viscosity. Comment: The old title "Modeling solid-fluid transformations in non-Newtonian viscoplastic flows with a unified flow theory" has been changed to the title of the published version "Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme" |
| Databáze: | OpenAIRE |
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