Some cases of numerical solution of differential equations describing the vortex-flow through three-dimensional axially symmetric channels

summary:In the article one partial differential equation of the second order is derived from the system of Euler's equations and the equation of continuity and it is solved by the finite-difference method, which gives good results

Stability of ALE space-time discontinuous Galerkin method

summary:We assume the heat equation in a time dependent domain, where the evolution of the domain is described by a given mapping. The problem is discretized by the discontinuous Galerkin (DG) method in space as well as in time with the aid of Arbitrary Lagrangian-Eulerian (ALE) method. The sketch of the proof of the stability of the method is shown

Discontinuous Galerkin method for compressible flow and conservation laws

summary:This paper is concerned with the application of the discontinuous Galerkin finite element method to the numerical solution of the compressible Navier-Stokes equations. The attention is paid to the derivation of discontinuous Galerkin finite element schemes and to the investigation of the accuracy of the symmetric as well as nonsymmetric discretization

On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains

summary:The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed

Numerical simulation of airfoil vibrations induced by turbulent flow

AbstractThe subject of this paper is the numerical simulation of the interaction between two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element solution of the Reynolds averaged Navier–Stokes equations with algebraic models of turbulence, coupled with the system of ordinary differential equations describing the airfoil motion. Since the computational domain is time dependent and the grid is moving, the Arbitrary Lagrangian–Eulerian (ALE) method is used. The developed method was applied to the simulation of flow-induced airfoil vibrations

Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition

summary:The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to the boundary corner points, the solution looses regularity in a vicinity of these points. It comes out that the error estimation depends essentially on the opening angle of the corner points and on the parameter defining the nonlinear behaviour of the Newton boundary condition. Theoretical results are compared with numerical experiments confirming a nonstandard behaviour of error estimates

Solution of elliptic problem with not fully specified Dirichlet boundary value conditions and its application in hydrodynamics

summary:The author solves a mixed boundary value problem for linear partial differential equations of the elliptic type in a multiply connected domain. Dirichlet conditions are given on the components of the boundary of the domain up to some additive constants which are not known a priori. These constants are to be determined, together with the solution of the boundary value problem, to fulfil some additional conditions. The results are immediately applicable in hydrodynamics to the solution of problems of stream fields round groups of profiles

Mathematical study of rotational incompressible non-viscous flows through multiply connected domains

summary:The paper is devoted to the study of the boundary value problem for an elliptic quasilinear second-order partial differential equation in a multiply connected, bounded plane domain under the assumption that the Dirichlet boundary value conditions on the separate components of the boundary are given up to additive constants. These constants together with the solution of the equation considered are to be determined so as to fulfil the so called trainling conditions. The results have immediate applications in the investigation of the rotational flow round groups of profiles or cascades of profiles