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This article presents results of an analysis of impact of a designed discharge of contaminated water into the Dead Vistula (Wisła Martwa) in the region of the Isthmus (Przesmyk) with the aim of determination of a possible effect of the pollution onto protected areas of Natura 2000 (bird habitats and sites, especially the Bird Paradise – Ptasi Raj) nature reserve. The analysis was conducted on the basis of the two-dimensional modelling of unsteady transport of non-degradable dissolved matter. To this end, a numerical model of a section of the Dead Vistula was worked out. Four scenarios of hydro-dynamical conditions (2 – for average weather conditions and 2 – for stormy weather conditions) were selected. To solving the equation of pollution migration the finite volumes method (MOS) was applied. Two localizations of contaminated water discharge outlet were considered, namely: the first from the side of Siennicki Bridge before the Isthmus and the other in the section of the Brave Vistula (Wisła Śmiała) downstream the Isthmus. The obtained results made it possible to assess positively the first localization of the designed discharge outlet. In the other case there is a fear that at unfavourable hydro-meteorological conditions a water pollution may happen over Natura 2000 protected areas.


Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

Finite-Volume Solvers for a Multilayer Saint-Venant System

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

.P. Il'in. High order accurate finite volumes discretization for Poisson equation. Siberian Math. J., 37(1), 151-169, 1996. [13] LeVeque and Z. Li. Erratum: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal, 32, 1704, 1995. [14] [15] Loudyi, D. Falconer, R.A. and Lin,B. Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications. Adv. Water Res., 30:29-42, 2007 [16]


Slushes are two-phase solid-liquid single-species cryogenic fluids that exhibit an increased density and a greater heat capacity with respect to the corresponding normal boiling point liquids. These promising features are of large interest for applications that exploit slush as a thermal fluid, like super magnets refrigeration, cryogenic cooling of bio-materials or air conditioning, and for aerospace systems that use slush fluids as fuel or oxidizer. Several programs in the frame of the research on Slush Hydrogen (SLH2) as a new-generation fuel for aerospace propulsion have been started in the past. This work was carried out in the framework of a VKI research activity promoted by the Predict ESA Technology Research Programme, to investigate experimentally and numerically the behavior of slush flows in a representative upper stage feeding line. In this paper, we present a simulation based on a granular two-fluid model on an isothermal solid liquid mixture (slurry) and a Nitrogen slush (SLN2) fluid flowing in a horizontal pipe. A finite-volumes discretization using the software library OpenFOAM was benchmarked against experimental and numerical literature data, to assess the accuracy of the code in predicting pressure drops along the pipe axis and solid particle distribution across the pipe diameter. Moreover, the effects of concentration and inlet velocity are investigated. We show that the numerical model fairly reproduces the literature data in terms of important aspects as the solid volume fraction distribution and the pressure drops, especially for high flow rates.


This paper presents general comments concerning investigations on water circulation in animal breeding pools containing sea water. As an example are given results of computer simulation of water circulation in seals′ breeding pools situated in Marine Station at Hel, belonging to Oceanographic Institute , Gdansk University. A mathematical model of three main pools was prepared with taking into account their inflow and outflow water supply points. Next, the object indication ( tracer) tests were done with the use of mathematical modelling as well as in-situ measurements. For description of flow field in steady conditions a simplified model of 2D flow in the form of Helmholtz biharmonic equation of stream function , recalculated then into velocity vector components, was used. The equation , supplemented with appropriate boundary conditions , was solved numerically by using the finite differences method. The spreading of a substance dissolved in water (tracer) was analyzed by solving 2D equation of transient advecting - dispersing transport. To solve it the finite volumes method was applied. The applied model was verified by conducting the indication tests with the use of the rhodamine WT as a tracer. The obtained results made it possible to reconstruct water circulation within the seals′ pools and identify stagnation zones in which water circulation may be made difficult.

.—LOCATI, M.—ALLAVENA, P.—SICA, A.: Macrophage polarization: tumor-associated macrophages as a paradigm for polarized M2 mononuclear phagocytes , Trends in Immunology 23 (2002), no. 11, 549–555. [8] MIKULA, K.—PEYRIÉRAS, N.—REMEŠIKOVÁ, M.—SARTI, A.: 3 D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique , Finite Volumes for Complex Applications V: Problems and Perspectives (2008), 585–592. [9] MIKULA, K.—URBÁN, J.—KOLLAR, M.—AMBROZ, M.—JAROLIMEK, I.—SIBIK J.—SIBIKOVA, M.: Semi-automatic segmentation of NATURA

. Neilan, and J.S. Ovall. A posteriori estimates using auxiliary subspace techniques. Journal of Scientific Computing , 72:97–127, 2017. [14] F. Hermeline. A finite volume method for approximating 3D diffusion operators on general meshes. J. Comput. Phys. , 228:5763–5786, 2009. [15] A. Mahamane. Analysis of the mixed finite volume scheme for a convection–diffusion equation. Finite Volumes for Complex Applications R. Eymard and J.-M. Hérard (eds) , V:569–576, 2008. [16] S. Nicaise. A posteriori error estimations of some cell centered finite volume methods for

for the generalized subjective surface equation in image segmentation ,Kybernetika 4 , no. 4 (2009), 646–656. [8] MIKULA, K.—PEYRIÉRAS, N.—REMEŠÍKOVÁ, M.—SARTI, A.: 3D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique .In: Finite Volumes for Complex Applications V: Problems and Perspectives (R. Eymard, J. M. Herard, eds.), ISTE and WILEY, London, 2008, pp. 585–592. [9] MIKULA, K.—PEYRIÉRAS, N.—REMEŠÍKOVÁ, M.—STAŠOVÁ, O.: Segmentation and analysis of 3D zebrafish cell image data .In: Proc. of the 3rd

. (2014), “Exploratory factor analysis: Concepts and theory”, in Balicki, J. (Ed.), Advances in Applied and Pure Mathematics, Proceedings of the 2nd International Conference on Mathematical, Computational and Statistical Sciences (MCSS '14); Proceedings of the 7th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements (F-and-B '14), Gdansk, Poland, WSEAS Press, pp. 375-382. 30. Tavakol, M., Dennick, R. (2011), “Making sense of Cronbach’s alpha”, International Journal of Medical Education, Vol. 2, pp. 53-55. 31. Teddlie, C., Yu