Algoritmy pro úlohy proudění se skluzovou okrajovou podmínkou ve třech prostorových dimenzích

Abstract

The diploma thesis deals with the Navier-Stokes problem solved using the finite element method in two and three spatial dimensions. It contains the formulation of the problem and its weak formulation with a stick-slip boundary condition. The resulting problem contains two nonlinearities. The first caused by the convective term is linearized by Ossen iterations and the second caused by the nonlinear stick-slip condition is solved by the semi-smooth Newton method. The convergence of the Ossen iterations in two and three space dimensions is checked. The following are experiments with different the preconditioners of the BiCGstab solver, which is used to solve internal problems within Ossen's and also Newton's iterations. The test were performed on different domains with different boundary conditions. The appendix describes the derivation of~vectorized algorithms for the construction of stiffness matrices and the right-hand vector of the Navier-stokes problem, where in addition to the basic linear basis functions, the bubble function is also used.