Numerical Simulation of Viscoelastic Fluids with Mesoscopic Models PDF Download

Author: John Cathal Bonvin
Publisher:
ISBN:
Category :
Languages : en
Pages : 159

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Author: Amr Guaily
Publisher: LAP Lambert Academic Publishing
ISBN: 9783846521007
Category :
Languages : en
Pages : 156

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Book Description
Although viscoelastic flows are characterized by a very low Mach number regime, it involves a weakly compressible liquid phase, which requires a special treatment. This work is devoted to the mathematical modeling and numerical simulation for viscoelastic fluids. It follows directly a previous publication, PhD dissertation of the author. A Unified purely hyperbolic mathematical model for compressible and incompressible viscoelastic fluids is presented. To complete the mathematical model, a complete chapter is devoted to describe a new procedure to determine the correct type and number of boundary conditions for hyperbolic systems. Then a new model describing the non-isothermal viscoelastic flows is introduced while keeping the hyperbolic nature of the system. The main advantage of the proposed model over the existing ones is its hyperbolic nature, which overcomes some of the drawbacks of the available models. The proposed model is then solved numerically using a hybrid finite element/finite difference scheme.

Author: Bangwei She
Publisher:
ISBN:
Category :
Languages : en
Pages : 103

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Author: Juan Enrique Santos
Publisher: Birkhäuser
ISBN: 3319484575
Category : Mathematics
Languages : en
Pages : 312

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This book presents the theory of waves propagation in a fluid-saturated porous medium (a Biot medium) and its application in Applied Geophysics. In particular, a derivation of absorbing boundary conditions in viscoelastic and poroelastic media is presented, which later is employed in the applications. The partial differential equations describing the propagation of waves in Biot media are solved using the Finite Element Method (FEM). Waves propagating in a Biot medium suffer attenuation and dispersion effects. In particular the fast compressional and shear waves are converted to slow diffusion-type waves at mesoscopic-scale heterogeneities (on the order of centimeters), effect usually occurring in the seismic range of frequencies. In some cases, a Biot medium presents a dense set of fractures oriented in preference directions. When the average distance between fractures is much smaller than the wavelengths of the travelling fast compressional and shear waves, the medium behaves as an effective viscoelastic and anisotropic medium at the macroscale. The book presents a procedure determine the coefficients of the effective medium employing a collection of time-harmonic compressibility and shear experiments, in the context of Numerical Rock Physics. Each experiment is associated with a boundary value problem, that is solved using the FEM. This approach offers an alternative to laboratory observations with the advantages that they are inexpensive, repeatable and essentially free from experimental errors. The different topics are followed by illustrative examples of application in Geophysical Exploration. In particular, the effects caused by mesoscopic-scale heterogeneities or the presence of aligned fractures are taking into account in the seismic wave propagation models at the macroscale. The numerical simulations of wave propagation are presented with sufficient detail as to be easily implemented assuming the knowledge of scientific programming techniques.

Author: Michael Renardy
Publisher: SIAM
ISBN: 0898714575
Category : Mathematics
Languages : en
Pages : 110

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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: Martinus A. Hulsen
Publisher:
ISBN: 9789062754946
Category : Viscoelasticity
Languages : en
Pages : 169

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Author: Theodore Finn Gast
Publisher:
ISBN:
Category :
Languages : en
Pages : 130

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Practical time steps in today's state-of-the-art simulators typically rely on Newton's method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. Recasting backward Euler as a minimization problem allows Newton's method to be stabilized by standard optimization techniques. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. Simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. Several collision formulations are presented including for self collisions and collisions against scripted bodies, which are designed for the unique demands of this solver. Finally the Material Point Method (MPM) can be formulated to use the solver, and we present formulations for its use for simulating various materials. For simulating viscoelastic fluids, foams and sponges, we design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd- B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). We show that implicit time stepping can be achieved with an optimization based approach and that this allows for high resolution simulations at practical simulation times. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit (non-optimization based) and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.

Author: Wan-Chi Tsai
Publisher:
ISBN: 9781124666464
Category :
Languages : en
Pages :

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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: Michael Griebel
Publisher: SIAM
ISBN: 0898719704
Category : Science
Languages : en
Pages : 217

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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.

Author: Roland Glowinski
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110785056
Category : Mathematics
Languages : en
Pages : 236

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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.