8 research outputs found

### Monolithic Finite Element Method for the simulation of thixo-viscoplastic flows

[EN] This note is concerned with the application of Finite Element Method (FEM) and NewtonMultigrid solver to simulate thixo-viscoplastic flows. The thixo-viscoplastic stress dependent on material microstructure is incorporated via viscosity approach into generalized Navier-Stokes equations.
The full system of equations is solved in a monolithic framework based on Newton-Multigrid FEM
Solver. The developed solver is used to analyze the thixo-viscoplastic flow problem in a Lid-driven
cavity configuration.The authors acknowledge the funding provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 446888252. Additionally, the authors acknowledge the financial grant provided by the Bundesministerium fr Wirtschaft und Energie aufgrund eines Beschlusses des Deutschen Bundestages through AiF-Forschungsvereinigung: Forschungs- Gesellschaft Verfahrens Technik e. V. - GVT under the IGF project number 20871 N. We would also like to gratefully acknowledge the support by LSIII and LiDO3 team at ITMC, TU Dortmund University, Germany.Begum, N.; Ouazzi, A.; Turek, S. (2022). Monolithic Finite Element Method for the simulation of thixo-viscoplastic flows. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat PolitĂ¨cnica de ValĂ¨ncia. 170-179. https://doi.org/10.4995/YIC2021.2021.12250OCS17017

### An adaptive discrete Newton method for regularization-free Bingham model

[EN] Developing a numerical and algorithmic tool which correctly identifies unyielded
regions in yield stress fluid flow is a challenging task. Two approaches are commonly used to
handle the singular behaviour at the yield surface, i.e. the Augmented Lagrangian approach and
the regularization approach, respectively. Generally in the regularization approach, solvers do
not perform efficiently when the regularization parameter gets very small. In this work, we use
a formulation introducing a new auxiliary stress. The three field formulation of the yield stress
fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations
arising from the three field formulation is solved efficiently and accurately by a monolithic finite
element method. The velocity and pressure are discretized by the higher order stable FEM pair
Q2/Pdisc
1 and the auxiliary stress is discretized by the Q2 element.
Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear
solver. Therefore, we developed a new adaptive discrete Newton method, which evaluates the
Jacobian with the divided difference approach. We relate the step length to the rate of the actual
nonlinear reduction for achieving a robust adaptive Newton method. We analyse the solvability
of the problem along with the adaptive Newton method for Bingham fluids by doing numerical
studies for a prototypical configuration â€ťviscoplastic fluid flow in a channelâ€ť.We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for their financial support under the DFG Priority Program SPP 1962. The authors also acknowledge the support by LS3 and LiDO3 team at ITMC, TU Dortmund UniversityFatima, A.; Turek, S.; Ouazzi, A.; Afaq, MA. (2022). An adaptive discrete Newton method for regularization-free Bingham model. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat PolitĂ¨cnica de ValĂ¨ncia. 180-189. https://doi.org/10.4995/YIC2021.2021.12389OCS18018

### Monolithic Newton-Multigrid Solver for Multiphase Flow Problems with Surface Tension

[EN] We have developed a monolithic Newton-multigrid solver for multiphase flow problems which solves velocity, pressure and interface position simultaneously. The main idea of our work is based on the formulations discussed in [1], where it points out the feasibility of a fully implicit monolithic solver for multiphase flow problems via two formulations, a curvature-free level set approach and a curvature-free cutoff material function approach. Both formulations are fully implicit and have the advantages of requiring less regularity, since neither normals nor curvature are explicitly calculated, and no capillary time restriction. Furthermore, standard Navier-Stokes solvers might be used, which do not have to take into account inhomogeneous force terms. The reinitialization issue is integrated with a nonlinear terms within the formulations.The nonlinearity is treated with a Newton-type solver with divided difference evaluation of the Jacobian matrices. The resulting linearized system inside of the outer Newton solver is a typical saddle point problem which is solved using the geometrical multigrid with Vanka-like smoother using higher order stable FEM pair $Q_2/P^{\text{disc}}_1$ for velocity and pressure and $Q_2$ for all other variables. The method is implemented into an existing software packages for the numerical simulation of multiphase flows (FeatFlow). The robustness and accuracy of this solver is tested for two different test cases, i.e. static bubble and oscillating bubble, respectively [2].Muhammad Aaqib Afaq would like to thank Erasmus Mundus INTACT project, funded by the European Union as part of the Erasmus Mundus programme and the National University of Sciences and Technology (NUST) for their financial support. The authors also acknowledge the support by LS3 and LiDO3 team at ITMC, TU Dortmund University.Afaq, MA.; Turek, S.; Ouazzi, A.; Fatima, A. (2022). Monolithic Newton-Multigrid Solver for Multiphase Flow Problems with Surface Tension. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat PolitĂ¨cnica de ValĂ¨ncia. 190-199. https://doi.org/10.4995/YIC2021.2021.12390OCS19019

### Finite Element Methods for the simulation of thixotropic flow problems

This note is concerned with the application of Finite Element Methods (FEM) and Newton-Multigrid solvers for the simulation of thixotropic flow problems. The thixotropy phenomena are introduced into viscoplastic material by taking into account the internal material micro structure using a scalar structure parameter. Firstly, the viscoplastic stress is modified to include the thixotropic stress dependent on the structure parameter. Secondly, an evolution equation for the structure parameter is introduced to induce the time-dependent process of competition between the destruction (breakdown) and the construction (buildup) inhabited in the material. Substantially, this is done simply by introducing a structure-parameter-dependent viscosity into the rheological model for yield stress material. The modified thixotropic viscoplastic stress w.r.t. the structure parameter is integrated in quasi-Newtonian manner into the generalized Navier-Stokes equations and the evolution equation for the structure parameter constitutes the main core of full set of modeling equations, which are creditable as the privilege answer to incorporate thixotropy phenomena. A fully coupled monolithic finite element approach has been exercised which manages the material internal micro structure parameter, velocity, and pressure fields simultaneously. The nonlinearity of the corresponding problem, related to the dependency of the diffusive stress on the material parameters and the nonlinear structure parameter models on the other hand, is treated with generalized Newton's method w.r.t. the Jacobian's singularities having a global convergence property. The linearized systems inside the outer Newton loops form a typical saddle-point problem which is solved using a geometrical multigrid method with a Vanka-like smoother taking into account a stable FEM approximation pair for velocity and pressure with discontinuous linear pressure and biquadratic velocity spaces. We examine the accuracy, robustness and efficiency of the Newton-Multigrid FEM solver throughout the solution of thixotropic viscoplastic flow problems in Couette device and in 4:1 contraction

### FEM analysis and monolithic Newton-multigrid solver for thixo-viscoplastic flow problems

In this contribution, we shall be concerned with the question of wellposedness of thixoviscoplastic flow problems in context of FEM approximations.We restrict our analysis to a quasiNewtonian modeling approach with the aim to set foundations for an efficient monolithic Newtonmultigrid solver. We present the wellposedness of viscoplastic subproblems and structure subproblems in parallel/independent fashion showing the possibility for a combined treatment. Then, we use the fixed point theorem for the coupled problem. For the numerical solutions, we choose 4:1 contraction configuration and use monolithic Newton-multigrid solver. We analyse the effect of taking into consideration thixotropic phenomena in viscoplastic material and opening up for more different coupling by inclusions of shear thickening and shear thinning behaviors for plastic viscosity and/or elastic behavior below the critical yield stress limit in more a general thixotropic models

### An Investigation on Separation Points of Power-Law model Along a Rotating Round-Nosed Body

The purpose of present study is to numerically investigate the natural convection flow of Ostwalde-de Waele type power law non-Newtonian fluid along the surface of rotating axi-symmetric round-nosed body. For computational purpose rotating hemisphere is used as a case study in order to examine the heat transfer mechanism near such transverse curvature geometries. The numerical scheme is applied after converting the dimensionless system of equations into primitive variable formulations. Implicit finite difference method is used to integrate the equations numerically. Its worth mentioning that all the numerical simulations performed here are valid particularly for the class of shear thickening fluid with wide range of Prandtl number, i.e. (10:0 â‰¤ Pr â‰¤ 1500:0). A detailed discussion is done to understand the effects of buoyant forces and power-law exponents on the rate of heat transfer and skin friction coefficient at the surface of the hemisphere. Comparison of present numerical results for different values of buoyancy ratio parameter Î» with other published data has been shown in graphical form. For the first time the velocity profiles are plotted at the point of separation, which occurs when the portion of the boundary layer closest to the wall or leading edge reverses in flow direction. It is recorded that an increase in the power-law index n and Prandtl number Pr leads to an increase in the friction factor as well as in the rate of heat transfer

### A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations

In the present contribution we compare different mixed least-squares finite element formula-tions (LSFEMs) with respect to computational costs and accuracy. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier-Stokes equa-tions. Starting from the residual forms of the equilibrium equation and the continuity condition, various first-order systems are derived. From these systems least-squares functionals are con-structed by means of L2-norms, which are the basis for the associated minimization problems. The first formulation under consideration is a div-grad first-order system resulting in a three-field formulation with stresses, velocities, and pressure as unknowns. This S-V-P formulation is approximated in H(div) Ă— H1 Ă— L2 on triangles and for comparison also in H1 Ă—H1 Ă— L2 on quadrilaterals. The second formulation is the well-known div-curl-grad first-order velocity-vorticity-pressure (V-V-P) formulation. Here all unknowns are approximated in H1 on quadri-laterals. Besides some numerical advantages, as e.g. an inherent symmetric structure of the system of equations and a directly available error estimator, it is known that least-squares methods have also a drawback concerning mass conservation, especially when lower-order ele