868 research outputs found
Non-axisymmetric instability of shear-banded Taylor-Couette flow
Recent experiments show that shear-banded flows of semi-dilute worm-like
micelles in Taylor-Couette geometry exhibit a flow instability in the form of
Taylor-like vortices. Here we perform the non-axisymmetric linear stability
analysis of the diffusive Johnson-Segalman model of shear banding and show that
the nature of this instability depends on the applied shear rate. For the
experimentally relevant parameters, we find that at the beginning of the stress
plateau the instability is driven by the interface between the bands, while
most of the stress plateau is occupied by the bulk instability of the
high-shear-rate band. Our work significantly alters the recently proposed
stability diagram of shear-banded flows based on axisymmetric analysis.Comment: 6 pages, 5 figures, main text and supplementary material; accepted to
Phys. Rev. Let
The second-generation Shifted Boundary Method and its numerical analysis
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L2-estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions
A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods
We introduce a polynomial spectral calculus that follows from the summation
by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus
to simplify the analysis of two multidimensional discontinuous Galerkin
spectral element approximations
Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows
We find three types of steady solutions and remarkable flow pattern
transitions between them in a two-dimensional wavy-walled channel for low to
moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical
simulations with spectral element method. The solutions are called
"convective", "transition", and "elastic" in ascending order of Wi. In the
convective region in the Re-Wi parameter space, the convective effect and the
pressure gradient balance on average. As Wi increases, the elastic effect
becomes suddenly comparable and the first transition sets in. Through the
transition, a separation vortex disappears and a jet flow induced close to the
wall by the viscoelasticity moves into the bulk; The viscous drag significantly
drops and the elastic wall friction rises sharply. This transition is caused by
an elastic force in the streamwise direction due to the competition of the
convective and elastic effects. In the transition region, the convective and
elastic effects balance. When the elastic effect dominates the convective
effect, the second transition occurs but it is relatively moderate. The second
one seems to be governed by so-called Weissenberg effect. These transitions are
not sensitive to driving forces. By the scaling analysis, it is shown that the
stress component is proportional to the Reynolds number on the boundary of the
first transition in the Re-Wi space. This scaling coincides well with the
numerical result.Comment: 33pages, 23figures, submitted to Physical Review
A spectral element reduced basis method in parametric CFD
We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios
Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives
We carry out a direct numerical simulation (DNS) study that reveals the
effects of polymers on statistically steady, forced, homogeneous, isotropic
fluid turbulence. We find clear manifestations of dissipation-reduction
phenomena: On the addition of polymers to the turbulent fluid, we obtain a
reduction in the energy dissipation rate, a significant modification of the
fluid energy spectrum, especially in the deep-dissipation range, a suppression
of small-scale intermittency, and a decrease in small-scale vorticity
filaments. We also compare our results with recent experiments and earlier DNS
studies of decaying fluid turbulence with polymer additives.Comment: consistent with the published versio
Equation of state and opacities for hydrogen atmospheres of magnetars
The equation of state and radiative opacities of partially ionized, strongly
magnetized hydrogen plasmas, presented in a previous paper [ApJ 585, 955
(2003), astro-ph/0212062] for the magnetic field strengths 8.e11 G < B < 3.e13
G, are extended to the field strengths 3.e13 G < B < 1.e15 G, relevant for
magnetars. The first- and second-order thermodynamic functions and radiative
opacities are calculated and tabulated for 5.e5 < T < 4.e7 K in a wide range of
densities. We show that bound-free transitions give an important contribution
to the opacities in the considered range of B in the outer neutron-star
atmosphere layers. Unlike the case of weaker fields, bound-bound transitions
are unimportant.Comment: 7 pages, 6 figures, LaTeX using emulateapj.cls (included). Accepted
by Ap
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations
Equilibrium analysis of an immersed rigid leaflet by the virtual element method
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the domain functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness), we identify sufficient conditions on the spring stiffness function for the existence (and uniqueness) of equilibrium positions. This study resorts to techniques from shape differential calculus. We propose a numerical technique that exploits the mesh flexibility of the Virtual Element Method (VEM). A (polygonal) computational mesh is generated by cutting a fixed background grid with the leaflet geometry, and the problem is then solved with stable VEM Stokes elements of degrees 1 and 2 combined with a bisection algorithm. We prove quasi-optimal error estimates and present a large array of numerical experiments to document the accuracy and robustness with respect to degenerate geometry of the proposed methodology
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