Digital Object Identifier (DOI) 10.1007/s002050100158 An Eulerian Description of Fluids Containing Visco-Elastic Particles

Abstract Equations governing the flow of fluid containing visco-hyperelastic particles are developed in an Eulerian framework. The novel feature introduced here is to write an evolution equation for the strain. It is envisioned that this will simplify numerical codes which typically compute the strain on Lagrangian meshes moving through Eulerian meshes. Existence results for the flow of linear visco-hyperelastic particles in a Newtonian fluid are established using a Galerkin scheme.

[1]  Daniel D. Joseph,et al.  Fundamentals of two-fluid dynamics , 1993 .

[2]  Claude Bardos,et al.  Mathematical Topics in Fluid Mechanics, Volume 1, Incompressible Models , 1998 .

[3]  F. Otto,et al.  Thermodynamically driven incompressible fluid mixtures , 1997 .

[4]  Morton E. Gurtin,et al.  Continuum theory of thermally induced phase transitions based on an order parameter , 1993 .

[5]  M. Gurtin,et al.  TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER , 1995, patt-sol/9506001.

[6]  P. Lions,et al.  Ordinary differential equations, transport theory and Sobolev spaces , 1989 .

[7]  L. Anand,et al.  A computational procedure for rate-independent crystal plasticity , 1996 .

[8]  Jacques Periaux,et al.  A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow , 2000 .

[9]  Jacques Periaux,et al.  A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies : Application to particulate flow , 1999 .

[10]  Feng Wang,et al.  A Conservative Eulerian Numerical Scheme for Elastoplasticity and Application to Plate Impact Problems , 1993, IMPACT Comput. Sci. Eng..

[11]  Chun Liu.  Dynamic theory for incompressible Smectic-A liquid crystals: Existence and regularity , 2000 .

[12]  Daniel D. Joseph,et al.  Mathematical theory and applications , 1993 .

[13]  Michael Renardy,et al.  Mathematical problems in viscoelasticity , 1987 .

[14]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[15]  J. Keller,et al.  Reaction-diffusion processes and evolution to harmonic maps , 1989 .

[16]  George J. Fix,et al.  Phase field methods for free boundary problems , 1982 .

[17]  R. Temam.  Navier-Stokes Equations , 1977 .

[18]  J. Keller,et al.  Fast reaction, slow diffusion, and curve shortening , 1989 .

[19]  S. Kružkov.  FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES , 1970 .

[20]  G. Caginalp.  An analysis of a phase field model of a free boundary , 1986 .

[21]  Jacques-Louis Lions,et al.  On Some Questions in Boundary Value Problems of Mathematical Physics , 1978 .

[22]  P. Hartman.  Ordinary Differential Equations , 1965 .

[23]  G. Caginalp,et al.  Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. , 1989, Physical review. A, General physics.

[24]  C. Truesdell,et al.  Linear Theories of Elasticity and Thermoelasticity , 1973 .

[25]  R. Showalter.  Monotone operators in Banach space and nonlinear partial differential equations , 1996 .

[26]  J. Lowengrub,et al.  Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Jie Li,et al.  Numerical Study of Flows of Two Immiscible Liquids at Low Reynolds Number , 2000, SIAM Rev..

[28]  Luc Tartar,et al.  Compensated compactness and applications to partial differential equations , 1979 .

[29]  Daniel D. Joseph,et al.  Fundamentals of Two-Fluid Dynamics: Part II: Lubricated Transport, Drops and Miscible Liquids , 1992 .

[30]  Sophia Demoulini.  Weak Solutions for a Class of Nonlinear Systems of Viscoelasticity , 2000 .

[31]  Daniel D. Joseph,et al.  Lubricated transport, drops and miscible liquids , 1993 .

[32]  Charles S. Peskin,et al.  Stability and Instability in the Computation of Flows with Moving Immersed Boundaries: A Comparison of Three Methods , 1992, SIAM J. Sci. Comput..