Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

Peshkov, Ilya; Dumbser, Michael; Boscheri, Walter; Romenski, Evgeniy; Chiocchetti, Simone; Ioriatti, Matteo

doi:10.1016/j.compfluid.2021.104963

Cited by 23 publications

(15 citation statements)

References 74 publications

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“…Let us note that, from (55), the turbulent viscosity, µ t , is a linear function in y. Gathering ( 51), (52), and (55), we observe that the initial condition for this test case reads…”

Section: Logarithmic Velocity Profilementioning

confidence: 94%

“…Validation of the methodology on unstructured meshes in the framework of laminar Newtonian and non-Newtonian flows is carried out by considering different rheologies for the Couette and Hagen-Poiseuille flows, and for the lid-driven cavity benchmark, similar to what was done in [52] for an alternative mathematical model for the description of non-Newtonian fluids. Furthermore, the flow of a non-Newtonian fluid around a circular cylinder is computed, in order to show the capability of the hybrid FV/FE method to deal also with more complex geometries thanks to the use of unstructured meshes.…”

Section: Non-newtonian Flowsmentioning

confidence: 99%

“…In this paper, we choose the second option, i.e., we regularize the constitutive model taking into account the regularization proposed in [49]. Further advances in the simulation of non-Newtonian fluids in the framework of Stokes and Navier-Stokes equations can be found in [48,50] and of the GPR model for continuum mechanics in [51,52].…”

Section: Introductionmentioning

confidence: 99%

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Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

2021

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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.

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“…Let us note that, from (55), the turbulent viscosity, µ t , is a linear function in y. Gathering ( 51), (52), and (55), we observe that the initial condition for this test case reads…”

Section: Logarithmic Velocity Profilementioning

confidence: 94%

Section: Non-newtonian Flowsmentioning

confidence: 99%

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Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

2021

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“…Apart of being a deformation measure, the frame field A e also encodes the orientational degrees of freedom of the material elements, e.g. see the computational results in [47,20,91]. The orientational degrees of freedom might be relevant for turbulence modeling [94] or anisotropic plasticity models [98].…”

Section: Governing Equations: the Gpr Model For Continuum Mechanicsmentioning

confidence: 99%

A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes

Boscheri,

Chiocchetti,

Peshkov

2021

Preprint

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A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first-order hyperbolic formulation of continuum fluid and solid mechanics, namely the Godunov-Pehskov-Romenski (GPR) model. The scheme provably respects the stiff relaxation limits of the continuous model at the fully discrete level, thus it is asymptotic preserving. Furthermore, the GCL is satisfied by a compatible discretization that makes use of a nodal solver to compute vertex-based fluxes that are used both for the motion of the computational mesh as well as for the time evolution of the governing PDEs. Second order of accuracy in space is achieved using a TVD piecewise linear reconstruction, while an implicit-explicit (IMEX) Runge-Kutta time discretization allows the scheme to obtain higher accuracy also in time. Particular care is devoted to the design of a stiff ODE solver, based on approximate analytical solutions of the governing equations, that plays a crucial role when the visco-plastic limit of the model is approached. We demonstrate the accuracy and robustness of the scheme on a wide spectrum of material responses covered by the unified continuum model that includes inviscid hydrodynamics, viscous heat conducting fluids, elastic and elasto-plastic solids in multidimensional settings.

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“…It constitutes a monolithic mathematical framework that encompasses the evolution of all considered materials and provides a unified mathematical description of multi-physics systems, see e.g. [33] for a generalization of the two-phase flow model given in [34,36] to an arbitrary number of phases, [13,30] for applications of the SHTC theory to fluid and solid mechanics modeling, or [35] for recent advances in the description of poroelastic fluid-saturated media.…”

Section: Introductionmentioning

confidence: 99%

An all Mach number finite volume method for isentropic two-phase flow

Lukáčová-Medviďová¹,

Puppo²,

Thomann³

2022

Preprint

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We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.

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Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

Cited by 23 publications

References 74 publications

Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes

An all Mach number finite volume method for isentropic two-phase flow

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