Author: Paul Joseph NortheyPublisher:
ISBN:
Category :
Languages : en
Pages : 584
Book Description
Numerical Simulation of Time-dependent, Two-dimensional Viscoelastic Fluid Flows
Author: Paul Joseph NortheyNumerical Simulation in Fluid Dynamics
Author: Michael GriebelPublisher: SIAM
ISBN: 9780898719703
Category : Science
Languages : en
Pages : 217
Book Description
In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as expository example, the individual steps of scientific computing are presented.
Numerical Simulation of Time Dependent Viscoelastic Fluid Flow
Author: Fredrik OlssonNumerical Simulation of Incompressible Viscous Flow
Author: Roland GlowinskiPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110785056
Category : Mathematics
Languages : en
Pages : 236
Book Description
This book on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to apply operator splitting techniques to decouple complicated computational fluid dynamics problems into a sequence of relatively simpler sub-problems at each time step, such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid. Efficient and robust numerical methods for solving those resulting simpler sub-problems are introduced and discussed. Interesting computational results are presented to show the capability of methodologies addressed in the book.
Numerical Simulation of Viscoelastic Fluid Flows by Spectral Element Methods and Time-dependent Algorithms
Author: Nicolas FiétierSimulation of Nonisothermal and Time-dependent Viscoelastic Flows
Author: Mark Davis SmithDirect Simulation of the Motion of Solid Particles in Viscoelastic Fluids
Author: Peter Yijian HuangNumerical Simulation of Hydrodynamically Developing Flow of a Nonlinear Viscoelastic Fluid
Author: Robert Eric GaidosPublisher:
ISBN:
Category : Differential equations, Nonlinear
Languages : en
Pages : 572
Book Description
Dynamics of Polymeric Liquids, Volume 2
Author: R. Byron BirdPublisher: Wiley-Interscience
ISBN: 9780471802440
Category : Technology & Engineering
Languages : en
Pages : 464
Book Description
This two-volume work is detailed enough to serve as a text and comprehensive enough to stand as a reference. Volume 1, Fluid Mechanics, summarizes the key experiments that show how polymeric fluids differ from structurally simple fluids, then presents, in rough historical order, various methods for solving polymer fluid dynamics problems. Volume 2, Kinetic Theory, uses molecular models and the methods of statistical mechanics to obtain relations between bulk flow behavior and polymer structure. Includes end-of-chapter problems and extensive appendixes.
Stabilized Finite Element Formulations for the Three-field Viscoelastic Fluid Flow Problem
Author: Ernesto Castillo del BarrioPublisher:
ISBN:
Category :
Languages : en
Pages : 214
Book Description
The Finite Element Method (FEM) is a powerful numerical tool, that permits the resolution of problems defined by partial differential equations, very often employed to deal with the numerical simulation of multiphysics problems. In this work, we use it to approximate numerically the viscoelastic fluid flow problem, which involves the resolution of the standard Navier-Stokes equations for velocity and pressure, and another tensorial reactive-convective constitutive equation for the elastic part of the stress, that describes the viscoelastic nature of the fluid. The three-field (velocity-pressure-stress) mixed formulation of the incompressible Navier-Stokes problem, either in the elastic and in the non-elastic case, can lead to two different types of numerical instabilities. The first is associated with the incompressibility and loss of stability of the stress field, and the second with the dominant convection. The first type of instabilities can be overcome by choosing an interpolation for the unknowns that satisfies the two inf-sup conditions that restrict the mixed problem, whereas the dominant convection requires a stabilized formulation in any case. In this work, different stabilized schemes of the Sub-Grid-Scale (SGS) type are proposed to solve the three-field problem, first for quasi Newtonian fluids and then for solving the viscoelastic case. The proposed methods allow one to use equal interpolation for the problem unknowns and to stabilize dominant convective terms both in the momentum and in the constitutive equation. Starting from a residual based formulation used in the quasi-Newtonian case, a non-residual based formulation is proposed in the viscoelastic case which is shown to have superior behavior when there are numerical or geometrical singularities. The stabilized finite element formulations presented in the work yield a global stable solution, however, if the solution presents very high gradients, local oscillations may still remain. In order to alleviate these local instabilities, a general discontinuity-capturing technique for the elastic stress is also proposed. The monolithic resolution of the three-field viscoelastic problem could be extremely expensive computationally, particularly, in the threedimensional case with ten degrees of freedom per node. A fractional step approach motivated in the classical pressure segregation algorithms used in the two-field Navier-Stokes problem is presented in the work.The algorithms designed allow one the resolution of the system of equations that define the problem in a fully decoupled manner, reducing in this way the CPU time and memory requirements with respect to the monolithic case. The numerical simulation of moving interfaces involved in two-fluid flow problems is an important topic in many industrial processes and physical situations. If we solve the problem using a fixed mesh approach, when the interface between both fluids cuts an element, the discontinuity in the material properties leads to discontinuities in the gradients of the unknowns which cannot be captured using a standard finite element interpolation. The method presented in this work features a local enrichment for the pressure unknowns which allows one to capture pressure gradient discontinuities in fluids presenting different density values. The stability and convergence of the non-residual formulation used for viscoelastic fluids is analyzed in the last part of the work, for a linearized stationary case of the Oseen type and for the semi-discrete time dependent non-linear case. In both cases, it is shown that the formulation is stable and optimally convergent under suitable regularity assumptions.