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On a constrained minimization problem arising in hemodynamics

João Janela, Adélia Sequeira (2008)

Banach Center Publications

Experimental evidence collected over the years shows that blood exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity, yield stress and thixotropic behaviour. Under certain conditions these characteristics become relevant and must be taken into consideration when modelling blood flow. In this work we deal with incompressible generalized Newtonian fluids, that account for the non-constant viscosity of blood, and present a new numerical method to handle fluid-rigid body interaction...

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Vít Dolejší, Miloslav Feistauer, Christoph Schwab (2002)

Mathematica Bohemica

The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite...

On equilibrium finite elements in three-dimensional case

Sergey Korotov (1997)

Applications of Mathematics

The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.

On evolution Galerkin methods for the Maxwell and the linearized Euler equations

Mária Lukáčová-Medviďová, Jitka Saibertová, Gerald G. Warnecke, Yousef Zahaykah (2004)

Applications of Mathematics

The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...

On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations

Xuejun Xu, C. O. Chow, S. H. Lui (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.

On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations

Xuejun Xu, C. O. Chow, S. H. Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.

On numerical solution of compressible flow in time-dependent domains

Miloslav Feistauer, Jaromír Horáček, Václav Kučera, Jaroslava Prokopová (2012)

Mathematica Bohemica

The paper deals with numerical simulation of a compressible flow in time-dependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous Galerkin finite element method (DGFEM) is used for the space semidiscretization of the governing equations...

On some Boussinesq systems in two space dimensions: theory and numerical analysis

Vassilios A. Dougalis, Dimitrios E. Mitsotakis, Jean-Claude Saut (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized...

On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations

R. Herbin, W. Kheriji, J.-C. Latché (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...

On stability of the P n mod / P n element for incompressible flow problems

Petr Knobloch (2006)

Applications of Mathematics

It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of n th order accuracy in the energy norm called P n elements. For n ≤ 3 we show that the stability condition holds if the velocity...

On the domain geometry dependence of the LBB condition

Evgenii V. Chizhonkov, Maxim A. Olshanskii (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The LBB condition is well-known to guarantee the stability of a finite element (FE) velocity - pressure pair in incompressible flow calculations. To ensure the condition to be satisfied a certain constant should be positive and mesh-independent. The paper studies the dependence of the LBB condition on the domain geometry. For model domains such as strips and rings the substantial dependence of this constant on geometry aspect ratios is observed. In domains with highly anisotropic substructures...

On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations

Vít Dolejší (2010)

Kybernetika

We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...

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