254 research outputs found
Flux form Semi-Lagrangian methods for parabolic problems
A semi-Lagrangian method for parabolic problems is proposed, that extends
previous work by the authors to achieve a fully conservative, flux-form
discretization of linear and nonlinear diffusion equations. A basic consistency
and convergence analysis are proposed. Numerical examples validate the proposed
method and display its potential for consistent semi-Lagrangian discretization
of advection--diffusion and nonlinear parabolic problems
A conservative implicit multirate method for hyperbolic problems
This work focuses on the development of a self adjusting multirate strategy
based on an implicit time discretization for the numerical solution of
hyperbolic equations, that could benefit from different time steps in different
areas of the spatial domain. We propose a novel mass conservative multirate
approach, that can be generalized to various implicit time discretization
methods. It is based on flux partitioning, so that flux exchanges between a
cell and its neighbors are balanced. A number of numerical experiments on both
non-linear scalar problems and systems of hyperbolic equations have been
carried out to test the efficiency and accuracy of the proposed approach
A fully semi-Lagrangian discretization for the 2D Navier--Stokes equations in the vorticity--streamfunction formulation
A numerical method for the two-dimensional, incompressible Navier--Stokes
equations in vorticity--streamfunction form is proposed, which employs
semi-Lagrangian discretizations for both the advection and diffusion terms,
thus achieving unconditional stability without the need to solve linear systems
beyond that required by the Poisson solver for the reconstruction of the
streamfunction. A description of the discretization of Dirichlet boundary
conditions for the semi-Lagrangian approach to diffusion terms is also
presented. Numerical experiments on classical benchmarks for incompressible
flow in simple geometries validate the proposed method
High order time integrators for the simulation of charged particle motion in magnetic quadrupoles
Magnetic quadrupoles are essential components of particle accelerators like
the Large Hadron Collider. In order to study numerically the stability of the
particle beam crossing a quadrupole, a large number of particle revolutions in
the accelerator must be simulated, thus leading to the necessity to preserve
numerically invariants of motion over a long time interval and to a substantial
computational cost, mostly related to the repeated evaluation of the magnetic
vector potential. In this paper, in order to reduce this cost, we first
consider a specific gauge transformation that allows to reduce significantly
the number of vector potential evaluations. We then analyze the sensitivity of
the numerical solution to the interpolation procedure required to compute
magnetic vector potential data from gridded precomputed values at the locations
required by high order time integration methods. Finally, we compare several
high order integration techniques, in order to assess their accuracy and
efficiency for these long term simulations. Explicit high order Lie methods are
considered, along with implicit high order symplectic integrators and
conventional explicit Runge Kutta methods. Among symplectic methods, high order
Lie integrators yield optimal results in terms of cost/accuracy ratios, but non
symplectic Runge Kutta methods perform remarkably well even in very long term
simulations. Furthermore, the accuracy of the field reconstruction and
interpolation techniques are shown to be limiting factors for the accuracy of
the particle tracking procedures.Comment: 39 pages, 18 figure
Flexible and efficient discretizations of multilayer models with variable density
We show that the semi-implicit time discretization approaches previously
introduced for multilayer shallow water models for the barotropic case can be
also applied to the variable density case with Boussinesq approximation.
Furthermore, also for the variable density equations, a variable number of
layers can be used, so as to achieve greater flexibility and efficiency of the
resulting multilayer approach. An analysis of the linearized system, which
allows to derive linear stability parameters in simple configurations, and the
resulting spatially semi-discretized equations are presented. A number of
numerical experiments demonstrate the effectiveness of the proposed approach
Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization
We propose an extension of the discretization approaches for multilayer
shallow water models, aimed at making them more flexible and efficient for
realistic applications to coastal flows. A novel discretization approach is
proposed, in which the number of vertical layers and their distribution are
allowed to change in different regions of the computational domain.
Furthermore, semi-implicit schemes are employed for the time discretization,
leading to a significant efficiency improvement for subcritical regimes. We
show that, in the typical regimes in which the application of multilayer
shallow water models is justified, the resulting discretization does not
introduce any major spurious feature and allows again to reduce substantially
the computational cost in areas with complex bathymetry. As an example of the
potential of the proposed technique, an application to a sediment transport
problem is presented, showing a remarkable improvement with respect to standard
discretization approaches
T-cells in myocardial infarction: Culprit instigators or mere effectors?
Immune system activation and dysfunction characterize the early phase of reperfusion after a myocardial infarction (MI). Despite initially neglected, adaptive immunity has been recently showed to play an important role in this setting. In fact, the immune system can recognize sequestered antigens released by the necrotic tissue, initiating a deleterious autoimmune vicious circle leading to worse outcome. In their recent work, Angelini et al shed the light on a new feature of post-MI which involves two "old players" of post-ischemic myocardial injury: CD31 and matrix metalloproteinase (MMP)-9. Specifically, the authors showed that an enhancement of MMP-9 release could determine the cleavage of inhibitory CD31 from CD4+ T-cells surface in patients with Acute Coronary Syndromes (ACS). These findings open the room for new studies investigating the role of MMP9 in other pathological processes associated with a reduction of CD31 functionality, such as plaque instability and rupture. Of interest, in the case of a causative role for CD31 shedding in ACS would be confirmed, there might be a potential role for the administration of CD31 protein or analogue compounds to blunt post-ischemic cardiac inflammation and improve ACS outcome
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