24,613 research outputs found
Dissipative Boussinesq equations
The classical theory of water waves is based on the theory of inviscid flows.
However it is important to include viscous effects in some applications. Two
models are proposed to add dissipative effects in the context of the Boussinesq
equations, which include the effects of weak dispersion and nonlinearity in a
shallow water framework. The dissipative Boussinesq equations are then
integrated numerically.Comment: 40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other
author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutyk
A numerically efficient finite element hydroelastic analysis
A finite element hydroelastic analysis formulation is developed on the basis of Toupin's complementary variational principle. Emphasis is placed on the special case of an incompressible fluid model which is applicable to propellant tank hydroelastic analysis. A concise fluid inertia representation results from the assumption of incompressibility and the hydroelastic equations reduce to a simplified form associated with the structure alone. The efficiency of the incompressible hydroelastic formulation in unhanced for both fluid and structure by introduction of harmonic reduction as an alternative to Guyan reduction. The theoretical developments are implemented in the NASTRAN Program and the technique is verified and demonstrated as an efficient and accurate approach with a series of illustrative problems including the 1/8 scale space shuttle external tank
Assumed-strain finite element technique for accurate modelling of plasticity problems
In this work a linear hexahedral element based on an assumed-strain finite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double- step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions
Visco-potential free-surface flows and long wave modelling
In a recent study [DutykhDias2007] we presented a novel visco-potential free
surface flows formulation. The governing equations contain local and nonlocal
dissipative terms. From physical point of view, local dissipation terms come
from molecular viscosity but in practical computations, rather eddy viscosity
should be used. On the other hand, nonlocal dissipative term represents a
correction due to the presence of a bottom boundary layer. Using the standard
procedure of Boussinesq equations derivation, we come to nonlocal long wave
equations. In this article we analyse dispersion relation properties of
proposed models. The effect of nonlocal term on solitary and linear progressive
waves attenuation is investigated. Finally, we present some computations with
viscous Boussinesq equations solved by a Fourier type spectral method.Comment: 29 pages, 13 figures. Some figures were updated. Revised version for
European Journal of Mechanics B/Fluids. Other author's papers can be
downloaded from http://www.lama.univ-savoie.fr/~dutyk
A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control
This paper is concerned with adaptive signal control problems on a road
network, using a link-based kinematic wave model (Han et al., 2012). Such a
model employs the Lighthill-Whitham-Richards model with a triangular
fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is
applied so that the system dynamics can be determined without knowledge of the
traffic state in the interior of each link. A Riemann problem for the
signalized junction is explicitly solved; and an optimization problem is
formulated in continuous-time with the aid of binary variables. A
time-discretization turns the optimization problem into a mixed integer linear
program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang,
2004; Lo, 1999b), the proposed framework does not require modeling or
computation within a link, thus reducing the number of (binary) variables and
computational effort.
The proposed model is free of vehicle-holding problems, and captures
important features of signalized networks such as physical queue, spill back,
vehicle turning, time-varying flow patterns and dynamic signal timing plans.
The MILP can be efficiently solved with standard optimization software.Comment: 15 pages, 7 figures, current version is accepted for presentation at
the 92nd Annual Meeting of Transportation Research Boar
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Moment Approximations and Model Cascades for Shallow Flow
Shallow flow models are used for a large number of applications including
weather forecasting, open channel hydraulics and simulation-based natural
hazard assessment. In these applications the shallowness of the process
motivates depth-averaging. While the shallow flow formulation is advantageous
in terms of computational efficiency, it also comes at the price of losing
vertical information such as the flow's velocity profile. This gives rise to a
model error, which limits the shallow flow model's predictive power and is
often not explicitly quantifiable.
We propose the use of vertical moments to overcome this problem. The shallow
moment approximation preserves information on the vertical flow structure while
still making use of the simplifying framework of depth-averaging. In this
article, we derive a generic shallow flow moment system of arbitrary order
starting from a set of balance laws, which has been reduced by scaling
arguments. The derivation is based on a fully vertically resolved reference
model with the vertical coordinate mapped onto the unit interval. We specify
the shallow flow moment hierarchy for kinematic and Newtonian flow conditions
and present 1D numerical results for shallow moment systems up to third order.
Finally, we assess their performance with respect to both the standard shallow
flow equations as well as with respect to the vertically resolved reference
model. Our results show that depending on the parameter regime, e.g. friction
and slip, shallow moment approximations significantly reduce the model error in
shallow flow regimes and have a lot of potential to increase the predictive
power of shallow flow models, while keeping them computationally cost
efficient
- …