An algorithm for approximation of an unsteady fluid-structure interaction problem is proposed. The fluid is governed by the Navier-Stokes equations with boundary conditions on pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary lagrangian Eulerian coordinates and the Finite Element Method for the fluid. In this paper, the continuity of the stresses at the interface was...

An algorithm for approximation of an unsteady fluid-structure interaction problem is proposed. The fluid is governed by the Navier-Stokes equations with boundary conditions on pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary Lagrangian Eulerian coordinates and the Finite Element Method for the fluid. In this paper, the continuity of the stresses at the interface...

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes...

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution algorithm...

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution...

This paper focuses on the mathematical modelling and the numerical approximation of the flow of two immiscible incompressible fluids. The surface tension effects are taken into account and mixed boundary conditions are used. The weak formulation is introduced, discretized in time, and the finite element method is applied. The free surface motion is treated with the aid of the level set method. The numerical results are shown.

We consider the mathematical modeling and numerical simulation of high throughput sorting of two different types of biological cells (type I and type II) by a biomedical micro-electro-mechanical system (BioMEMS) whose operating behavior relies on surface acoustic wave (SAW) manipulated fluid flow in a microchannel. The BioMEMS consists of a separation channel with three inflow channels for injection of the carrier fluid and the cells, two outflow channels for separation, and an interdigital transducer...

This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.

This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.

This work is concerned with the numerical solution of a hydrodynamic model of the macroscopic behavior of flocks of birds due to Fornasier et al., 2011. The model consists of the compressible Euler equations with an added nonlocal, nonlinear right-hand side. As noticed by the authors of the model, explicit time schemes are practically useless even on very coarse grids in 1D due to the nonlocal nature of the equations. To this end, we apply a semi-implicit discontinuous Galerkin method to solve the...

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing...

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for...

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines.

We consider the numerical solution of diffusion problems in $(0,T)\times \Omega$ for $\Omega \subset {ℝ}^d$ and for $T\>0$ in dimension $d\ge 1$. We use a wavelet based sparse grid space discretization with mesh-width $h$ and order $p\ge 1$, and $hp$ discontinuous Galerkin time-discretization of order $r=O\left(\left|logh\right|\right)$ on a geometric sequence of $O\left(\left|logh\right|\right)$ many time steps. The linear systems in each time step are solved iteratively by $O\left(\left|logh\right|\right)$ GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an $L^2\left(\Omega \right)$-error of $O\left(N^{-p}\right)$ for $u(x,T)$ where $N$ is the total number of operations,...

We consider the numerical solution of diffusion problems in (0,T) x Ω for $\Omega \subset {ℝ}^d$ and for T > 0 in dimension dd ≥ 1. We use a wavelet based sparse grid space discretization with mesh-width h and order pd ≥ 1, and hp discontinuous Galerkin time-discretization of order $r=O\left(\left|logh\right|\right)$ on a geometric sequence of $O\left(\left|logh\right|\right)$ many time steps. The linear systems in each time step are solved iteratively by $O\left(\left|logh\right|\right)$ GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...

A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...