Aleksey Sikstel

In this work, we devise a model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model consists of a system of hyperbolic balance laws with stiff reaction terms and the coarse model consists of a system of hyperbolic conservation laws. We employ the relative entropy stability...

This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer the system towards a desired state. The presented approach is based on a Lyapunov stability analysis and a CWEN...

This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haar sequence has been used by Pettersson, Iaccarino, Nordstroem (2014) for a hyperbolic stochastic Galerkin formulation of the one-dimensional Euler equations. This work ge...

This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer the system towards a desired state. The presented approach is based on a Lyapunov stability analysis and a CWEN...

We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulat...

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin (DG) schemes for hyperbolic conservation laws has been developed. The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids. Typically this concept is applied to dyadic grid hierarchies where...

The modelling of gas networks requires the development of coupling techniques at junctions. Recent work on the coupling of hyperbolic systems based on solving two half Riemann problems can be useful also for the coupling issue in gas networks. This strategy is exemplified here for the coupling of a fluid with a solid modelled by the Euler equations...

In Gerhard et al. (2015a) a new class of adaptive Discontinuous Galerkin schemes has been introduced for shallow water equations, including the particular necessary properties, such as well-balancing and wetting-drying treatments. The adaptivity strategy is based on multiresolution analysis using multiwavelets in order to encode information across...

We analyze properties of stochastic hyperbolic systems using a Galerkin formulation, which reformulates the stochastic system as a deterministic one that describes the evolution of polynomial chaos modes. We investigate conditions such that the resulting systems are hyperbolic. We state the eigendecompositions in closed form. A Roe flux is presente...

The Riemann problem for coupled Euler equations is analysed. The coupling conditions at a steady interface impose continuous pressure and temperature while momentum differs. The outtake of the momentum models the influence of a gas-powered generator linked to a high-pressure gas network. We prove the existence and uniqueness of the solution to the...