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This paper deals with the state estimation of non-linear stochastic dynamic systems, both continuous and discrete in time, with an emphasis on a numerical solution to the Bayesian relations by the point-mass filters. The filters for discrete-discrete and continuous-discrete state-space models are reviewed and a new highly accurate and fast active flux method is introduced and adapted for a continuous filter design. A wide set of the point-mass filters is compared in a numerical study together with a set of the particle filters.

The article is devoted to the simulation of viscous incompressible turbulent fluid flow based on solving the Reynolds averaged Navier-Stokes (RANS) equations with different k − ω models. The isogeometrical approach is used for the discretization based on the Galerkin method. Primary goal of using isogeometric analysis is to be always geometrically exact, independent of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization SUPG technique in equations for k and ω. The solutions are compared with the standard benchmark example of turbulent flow over a backward facing step.

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