Author: Wan-Chi Tsai Publisher: ISBN: 9781124666464 Category : Languages : en Pages :
Book Description
This thesis presents a numerical algorithm to simulate viscoelastic fluids in two dimensional problems. The incompressible Navier-Stokes equations, coupled with the multiple mode Giesekus constitutive equation for viscoelastic stress, are used to model viscoelastic fluids in our problem. A second order Godunov method is applied to compute edge-centered, time centered primitive variables as predictors for conservative flux differences, and the correctors are cell-centered conservative variables calculated by applying a conservative update equation including conservative source terms. For the stress equations, we apply a splitting technique which separates the viscoelastic stress into a viscous stress part (elliptic) and an elastic stress part (hyperbolic), and constructan artificial wave speed to slow down the system velocity and increase the CFL stable time step. In addition, the nonlinear stress source term is computed separately by applying an operator splitting method with a new, stable, discretization. This method is second order accurate in time and space, and captures the appropriate viscous and elastic limits. A projection method (BCG method) is used to enforce the velocity incompressibility constraint at edge-centered and cell-centered states. Since there is no longitudinal mode (P-wave mode) in incompressible flow, the double projection method is used to eliminate the longitudinal mode in the extra stress field.
Author: Wan-Chi Tsai Publisher: ISBN: 9781321023800 Category : Languages : en Pages :
Book Description
We present a convergent and stable numerical algorithm to simulate unsteady incompressible viscoelastic flow in two dimensional complex geometry. The incompressible viscous momentum equation, coupled with the multiple mode Giesekus constitutive equation for viscoelastic stress, are used to model viscoelastic fluids in our problems. We recast the hyperbolic part of equations to a second order conservative finite difference method and leave the elliptic part as a source term to be computed by implicit methods. A second order Godunov method is introduced to compute edge-centered, time-centered primitive variables for calculating fluxes in a conservative finite difference equation, and then cell-centered conservative variables are updated using a hybrid flux divergence and source terms. The nonlinear stress source term in the elliptic part is computed separately by applying an operator splitting method with a new, stable, discretization. A projection method is used to enforce the velocity incompressibility constraint and to update pressure. Irregular computational domains are discretized with a Cartesian grid embedded boundary method. We demonstrate our numerical method by computing flow passing a sphere, flow in a well-rounded contraction channel, and in an abrupt contraction channel, with component Weissenberg numbers exceeding 300. The convergence rates of the solution error are second order in the L1 and L2 norms, and first order in the L[infinity] norm for velocity components in arbitrary smooth geometries. For stress components, this numerical algorithm showed second order convergence rate in the L1 norm, higher than first order in the L2 norm.
Author: Michael Renardy Publisher: SIAM ISBN: 0898714575 Category : Mathematics Languages : en Pages : 110
Book Description
This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.
Author: J.F. Dijksman Publisher: Springer Science & Business Media ISBN: 9401101914 Category : Science Languages : en Pages : 200
Book Description
During the last decades a considerable effort has been made on the computation of the isothermal flow of viscoelastic fluids. In fact the activities related to this particular field of non-Newtonian fluid mechanics have focused on the following questions: which type of constitutive equation describes non-Newtonian fluid behaviour; how to measure fluid parameters; and what type of computational scheme leads to reliable, stable and cost-effective computer programs. During the same period, typical non-Newtonian fluid phenomena have been experimentally examined, such as the flow through a `four-to-one' contraction, the flow around a sphere or separation flow, providing fresh challenges for numerical modellers. Apart from momentum transport, however, fluid flow is strongly influenced by heat treansport in most real industrial operations in which non-Newtonian fluids are processed. The IUTAM Symposium on `Numerical Simulation of Nonisothermal Flow of Viscoelastic Liquids' held at Rolduc Abbey in Kerkrade, the Netherlands, November 1--3, 1993, was organised to monitor the state of affairs in regard to the influence of nonisothermal effects on the flow of a viscoelastic liquid. The present collection of papers gives an overview of what has been achieved so far. It is a milestone in the rapidly emerging and exciting new field in non-Newtonian fluid mechanics.
Author: Roland Glowinski Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110785013 Category : Mathematics Languages : en Pages : 232
Book Description
This text on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to split complicated computational fluid dynamics problems into a sequence of simpler sub-problems. A methodology for solving more advanced applications such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid is also presented.
Author: Robert G Owens Publisher: World Scientific ISBN: 1783261951 Category : Mathematics Languages : en Pages : 437
Book Description
Modern day high-performance computers are making available to 21st-century scientists solutions to rheological flow problems of ever-increasing complexity. Computational rheology is a fast-moving subject — problems which only 10 years ago were intractable, such as 3D transient flows of polymeric liquids, non-isothermal non-Newtonian flows or flows of highly elastic liquids through complex geometries, are now being tackled owing to the availability of parallel computers, adaptive methods and advances in constitutive modelling.Computational Rheology traces the development of numerical methods for non-Newtonian flows from the late 1960's to the present day. It begins with broad coverage of non-Newtonian fluids, including their mathematical modelling and analysis, before specific computational techniques are discussed. The application of these techniques to some important rheological flow problems of academic and industrial interest is then treated in a detailed and up-to-date exposition. Finally, the reader is kept abreast of topics at the cutting edge of research in computational applied mathematics, such as adaptivity and stochastic partial differential equations.All the topics in this book are dealt with from an elementary level and this makes the text suitable for advanced undergraduate and graduate students, as well as experienced researchers from both the academic and industrial communities.
Author: Wan-Chi Tsai
Author: Wan-Chi Tsai
Author: Michael Renardy
Author: Antony N. Beris
Author: J.F. Dijksman
Author: Roland Glowinski
Author: Martinus A. Hulsen
Author: Robert G Owens
Author: International Workshop on Numerical Simulation of Viscoelastic Flows
Author: Michael Aaron Mendelson