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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...

On energy conservation of the simplified Takahashi-Imada method

Ernst Hairer, Robert I. McLachlan, Robert D. Skeel (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy to implement...

On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis

Vlasák, Miloslav, Roskovec, Filip (2015)

Programs and Algorithms of Numerical Mathematics

Discontinuous Galerkin (DG) methods are starting to be a very popular solver for stiff ODEs. To be able to prove some more subtle properties of DG methods it can be shown that the DG method is equivalent to a specific collocation method which is in turn equivalent to an even more specific implicit Runge-Kutta (RK) method. These equivalences provide us with another interesting view on the DG method and enable us to employ well known techniques developed already for any of these methods. Our aim will...

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...

On those ordinary differential equations that are solved exactly by the improved Euler method

Hans Jakob Rivertz (2013)

Archivum Mathematicum

As a numerical method for solving ordinary differential equations y ' = f ( x , y ) , the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for f ( x , y ) to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method....

One-step methods for ordinary differential equations with parameters

Tadeusz Jankowski (1990)

Aplikace matematiky

In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.

Order conditions for partitioned Runge-Kutta methods

Zdzisław Jackiewicz, Rossana Vermiglio (2000)

Applications of Mathematics

We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.

Currently displaying 61 – 80 of 106