246 research outputs found
Global regularity properties of steady shear thinning flows
In this paper we study the regularity of weak solutions to systems of
p-Stokes type, describing the motion of some shear thinning fluids in certain
steady regimes. In particular we address the problem of regularity up to the
boundary improving previous results especially in terms of the allowed range
for the parameter p
Finite element approximation of an incompressible chemically reacting non-Newtonian fluid
We consider a system of nonlinear partial differential equations modelling
the steady motion of an incompressible non-Newtonian fluid, which is chemically
reacting. The governing system consists of a steady convection-diffusion
equation for the concentration and the generalized steady Navier-Stokes
equations, where the viscosity coefficient is a power-law type function of the
shear-rate, and the coupling between the equations results from the
concentration-dependence of the power-law index. This system of nonlinear
partial differential equations arises in mathematical models of the synovial
fluid found in the cavities of moving joints. We construct a finite element
approximation of the model and perform the mathematical analysis of the
numerical method in the case of two space dimensions. Key technical tools
include discrete counterparts of the Bogovski\u{\i} operator, De Giorgi's
regularity theorem in two dimensions, and the Acerbi-Fusco Lipschitz truncation
of Sobolev functions, in function spaces with variable integrability exponents.Comment: 40 page
On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index
Steady flows of an incompressible homogeneous chemically reacting fluid are
described by a coupled system, consisting of the generalized Navier--Stokes
equations and convection - diffusion equation with diffusivity dependent on the
concentration and the shear rate. Cauchy stress behaves like power-law fluid
with the exponent depending on the concentration. We prove the existence of a
classical solution for the two dimensional periodic case whenever the power law
exponent is above one and less than infinity
Global regularity for systems with -structure depending on the symmetric gradient
In this paper we study on smooth bounded domains the global regularity (up to
the boundary) for weak solutions to systems having -structure depending only
on the symmetric part of the gradient.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1607.0629
Implicit-explicit schemes for incompressible flow problems with variable viscosity
In this work we study different Implicit-Explicit (IMEX) schemes for
incompressible flow problems with variable viscosity. Unlike most previous work
on IMEX schemes, which focuses on the convective part, we here focus on
treating parts of the diffusive term explicitly to reduce the coupling between
the velocity components. We present different, both monolithic and
fractional-step, IMEX alternatives for the variable-viscosity Navier--Stokes
system, analysing their theoretical and algorithmic properties. Stability
results are proven for all the methods presented, with all these results being
unconditional, except for one of the discretisations using a fractional-step
scheme, where a CFL condition (in terms of the problem data) is required for
showing stability. Our analysis is supported by a series of numerical
experiments
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