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Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect...
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the...
We analyse Bérenger’s split algorithm applied to the system version of the two dimensional wave equation with absorptions equal to Heaviside functions of , . The methods form the core of the analysis [11] for three dimensional Maxwell equations with absorptions not necessarily piecewise constant. The split problem is well posed, has no loss of derivatives (for divergence free data in the case of Maxwell), and is perfectly matched.
Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically...
We present the fiber-spring elastic model of the arterial wall with atherosclerotic
plaque composed of a lipid pool and a fibrous cap. This model allows us to reproduce
pressure to cross-sectional area relationship along the diseased vessel which is used in
the network model of global blood circulation. Atherosclerosis attacks a region of
systemic arterial network. Our approach allows us to examine the impact of the diseased
region onto global haemodynamics....
Non reflecting boundary conditions on artificial frontiers
of the domain are proposed for both
incompressible and compressible Navier-Stokes equations.
For incompressible flows, the boundary conditions lead to a well-posed
problem, convey properly the vortices without any reflections on the
artificial limits and allow to compute turbulent flows at high Reynolds
numbers.
For compressible flows, the boundary conditions convey properly the
vortices without any reflections on the artificial limits...
We consider space semi-discretizations of the 1-d wave equation in a bounded
interval with homogeneous Dirichlet boundary conditions. We analyze the problem
of boundary observability, i.e., the problem of whether the total energy of
solutions can be estimated uniformly in terms of the energy concentrated on the
boundary as the net-spacing h → 0. We prove that, due to the spurious modes
that the numerical scheme introduces at high frequencies, there is no such a
uniform bound. We prove however a...
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