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Numerical modelling of viscous and viscoelastic fluids flow through the branching channel

Keslerová, Radka, Kozel, Karel (2015)

Programs and Algorithms of Numerical Mathematics

The aim of this paper is to describe the numerical results of numerical modelling of steady flows of laminar incompressible viscous and viscoelastic fluids. The mathematical models are Newtonian and Oldroyd-B models. Both models can be generalized by cross model in shear thinning meaning. Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method...

Numerical simulation of generalized Newtonian fluids flow in bypass geometry

Keslerová, Radka, Řezníček, Hynek, Padělek, Tomáš (2019)

Programs and Algorithms of Numerical Mathematics

The aim of this work is to present numerical results of non-Newtonian fluid flow in a model of bypass. Different angle of a connection between narrowed channel and the bypass graft is considered. Several rheology viscosity models were used for the non-Newtonian fluid, namely the modified Cross model and the Carreau-Yasuda model. The results of non-Newtonian fluid flow are compared to the results of Newtonian fluid. The fundamental system of equations is the generalized system of Navier-Stokes equations...

Numerical simulation of the motion of a three-dimensional glacier

Marco Picasso, Jacques Rappaz, Adrian Reist (2008)

Annales mathématiques Blaise Pascal

The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared to experiments...

Numerical simulations for nodal domains and spectral minimal partitions

Virginie Bonnaillie-Noël, Bernard Helffer, Gregory Vial (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We recall here some theoretical results of Helffer et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.

Numerical solution of parabolic equations in high dimensions

Tobias Von Petersdorff, Christoph Schwab (2004)

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

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

Numerical solution of parabolic equations in high dimensions

Tobias von Petersdorff, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the numerical solution of diffusion problems in (0,T) x Ω for Ω ⊂ 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 ( log h ) on a geometric sequence of O ( log h ) many time steps. The linear systems in each time step are solved iteratively by O ( log h ) GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...

Numerical solutions for second-kind Volterra integral equations by Galerkin methods

Shu Hua Zhang, Yan Ping Lin, Ming Rao (2000)

Applications of Mathematics

In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...

Numerical studies of groundwater flow problems with a singularity

Hokr, Milan, Balvín, Aleš (2017)

Programs and Algorithms of Numerical Mathematics

The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...

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