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Item type:Publication, Access status: without files , Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry frontsThe aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG methods couple a finite volume formulation with evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems. However, in the case of multilayer shallow water flows the required eigenstructure of the underlying equations is not readily available. Thus we approximate the evolution operators numerically. This approximation procedure can be used for arbitrary hyperbolic systems. We derive a well-balanced approximation of the evolution operators and prove that the FVEG scheme is well-balanced for the multilayer lake at rest states even in the presence of wet/dry fronts. Several numerical experiments confirm the reliability and efficiency of the new well-balanced FVEG scheme.Publicationtype: Journal Article105 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Well-balanced path-consistent finite volume eg schemes for the two-layer shallow water equationsWe present a new path-consistent well-balanced finite volume method within the framework of the evolution Galerkin (FVEG) schemes. The methodology will be illustrated for two layer shallow water equations with source terms modelling the bottom topography and Coriolis forces. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We will derive a suitable path in the phase space that is based on the evolution operator and derive the corresponding path-consistent FVEG scheme. The path-consistent FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame.Publicationtype: Conference Paper6 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Numerical study of shear-dependent non-Newtonian fluids in compliant vesselsThe aim of this contribution is to present recent results on numerical modelling of non-Newtonian flow in compliant stenosed vessels with application in hemodynamics. We consider two models of shear-thinning non-Newtonian fluids and compare them with the Newtonian model. For the structure problem, the generalized string equation for radial symmetric tubes is used and extended to a stenosed vessel. The global iterative approach to approximate the fluidstructure interaction is used. Finally, we present numerical experiments for some non-Newtonian models, comparisons with the Newtonian model and the results for hemodynamic wall parameters such as the wall shear stress and the oscillatory shear index.Publicationtype: Journal Article131 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Validation of a spatially interconnected model for plane poiseuille flow transition controlA novel linearized model for the transition control problem in plane Poiseuille flow has been proposed recently. The model is based on a finite difference approach in streamwise direction and a spectral approach in wall normal direction. It is thus valid for all spatial frequencies and can be used for the synthesis of controllers for flow control problems, using recently developed ideas for spatially interconnected systems. In this paper the above model is validated in both time and frequency domain. For time domain validation, the transient energy is calculated and compared with previously published results. The frequency domain validation is based on nonlinear simulation: a sinusoidal disturbance is applied at the lower boundary and its effect at different locations of the channel are simulated. From a Fourier analysis of the simulated responses, the spatial and temporal frequency responses are obtained and compared with the linearized model. The results suggest that the model captures the dominant features of the problem and can be used for the design of spatially interconnected controllers.Publicationtype: Conference Paper31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On the stability of evolution Galerkin schemes applied to a two-dimensional wave equation systemThe subject of the paper is the analysis of stability of the evolution Galerkin (EG) methods for the two-dimensional wave equation system. We apply von Neumann analysis and use the Fourier transformation to estimate the stability limits of both the first and the second order EG methods.Publicationtype: Journal Article413 618 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Well-balanced finite volume evolution Galerkin methods for the shallow water equations(2005-05); ; We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We derive a well-balanced approximation of the integral equations and prove that the FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. Several numerical experiments for stationary and quasi-stationary states as well as for steady jets confirm the reliability of the well-balanced FVEG scheme.Publicationtype: PreprintScopus© Citations 63 508 403 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Comparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction terms(2005-03); We present a comparison of two discretization methods for the shallow water equations, namely the finite volume method and the finite element scheme. A reliable model for practical interests includes terms modelling the bottom topography as well as the friction effects. The resulting equations belong to the class of systems of hyperbolic partial differential equations of first order with zero order source terms, the so-called balance laws. In order to approximate correctly steady equilibrium states we need to derive a well-balanced approximation of the source term in the finite volume framework. As a result our finite volume method, a genuinely multidimensional finite volume evolution Galerkin (FVEG) scheme, approximates correctly steady states as well as their small perturbations (quasi-steady states). The second discretization scheme, which has been used for practical river flow simulations, is the finite element method (FEM). In contrary to the FVEG scheme, which is a time explicit scheme, the FEM uses an implicite time discretization and the Newton-Raphson iterative scheme for inner iterations. We compare the accuracy and performance of both scheme through several numerical experiments, which demonstrate the reliability of both discretization techniques and correct approximation of quasisteady states with bottom topography and friction.Publicationtype: PreprintScopus© Citations 14 555 454 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Numerical modeling of shallow flows including bottom topography and friction effects(2004-11)The aim of the paper is numerical modeling of the shallow water equation with source terms by genuinely multdimensional finite volume evolution Galerkin schemes. The shallow water system, or its one-dimensional analogy the Saint-Venant equation, is used extensively for numerical simulation of natural rivers. Mathematically the shallow water system belongs to the class of balance laws. A special treatment of the source terms describing the bottom topography as well as frictions effects is necessary in order to reflect their balance with the gradients of fluxes. We present behaviour of our new well-balance FVEG scheme for several benchmark test problems and compare our results with those obtained by the finite element scheme of Teschke et al. used for practical river simulations.Publicationtype: Preprint276 224 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation systemThe subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutions. Moreover, we construct further new EG schemes by neglecting the so-called source term, i.e. we mimic Kirchhoff's formula. The numerical test shows that such schemes are more accurate and some of them are of second order.Publicationtype: PreprintScopus© Citations 5 554 554 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics(2004-09); In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics of multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self contained overview on the recent results. We study the L1-stability of the finite volume schemes obtained by different approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.Publicationtype: PreprintScopus© Citations 9 372 210