Nelida Črnjarić-Žic

Dynamic autoinoculation and the microbial ecology of a deep water hydrocarbon irruption

The irruption of gas and oil into the Gulf of Mexico during the Deepwater Horizon event fed a deep sea bacterial bloom that consumed hydrocarbons in the affected waters, formed a regional oxygen anomaly, and altered the microbiology of the region. In this work, we develop a coupled physical–metabolic model to assess the impact of mixing processes on these deep ocean bacterial communities and their capacity for hydrocarbon and oxygen use. We find that observed biodegradation patterns are well-described by exponential growth of bacteria from seed populations present at low abundance and that current oscillation and mixing processes played a critical role in distributing hydrocarbons and associated bacterial blooms within the northeast Gulf of Mexico. Mixing processes also accelerated hydrocarbon degradation through an autoinoculation effect, where water masses, in which the hydrocarbon irruption had caused blooms, later returned to the spill site with hydrocarbon-degrading bacteria persisting at elevated abundance. Interestingly, although the initial irruption of hydrocarbons fed successive blooms of different bacterial types, subsequent irruptions promoted consistency in the structure of the bacterial community. These results highlight an impact of mixing and circulation processes on biodegradation activity of bacteria during the Deepwater Horizon event and suggest an important role for mixing processes in the microbial ecology of deep ocean environments.

Extension of ENO and WENO schemes to one-dimensional sediment transport equations

Essentially nonoscillatory and weighted essentially nonoscillatory schemes are high order resolution schemes constructed for the hyperbolic conservation laws. In this paper we extend these schemes to the one-dimensional bed-load sediment transport equations. The difficulties that arise in the numerical modelling come from the fact that a nonconservative product is present in the system. Our specific numerical approximations for the nonconservative product are based on two ideas. First is to include the influence of that term in the system upwinding and the second is to define the numerical approximation in such a way that the obtained scheme solves the system for the quiescent flow case exactly. As a consequence, the resulting schemes give excellent results, as it can be seen from the numerical tests we present. On the opposite, the numerical results obtained by applying the pointwise evaluation of nonconservative product on the same tests present unacceptably large numerical errors.

High order accurate semi-implicit WENO schemes for hyperbolic balance laws

Abstract In this paper we propose a family of well-balanced semi-implicit numerical schemes for hyperbolic conservation and balance laws. The basic idea of the proposed schemes lies in the combination of the finite volume WENO discretization with Roe’s solver and the strong stability preserving (SSP) time integration methods, which ensure the stability properties of the considered schemes [S. Gottlieb, C.-W. Shu, E. Tadmor, Strong stability-preserving high-order time discretization methods, SIAM Rev. 43 (2001) 89–112]. While standard WENO schemes typically use explicit time integration methods, in this paper we are combining WENO spatial discretization with optimal SSP singly diagonally implicit (SDIRK) methods developed in [L. Ferracina, M.N. Spijker, Strong stability of singly diagonally implicit Runge–Kutta methods, Appl. Numer. Math. 58 (2008) 1675–1686]. In this way the implicit WENO numerical schemes are obtained. In order to reduce the computational effort, the implicit part of the numerical scheme is linearized in time by taking into account the complete WENO reconstruction procedure. With the proposed linearization the new semi-implicit finite volume WENO schemes are designed. A detailed numerical investigation of the proposed numerical schemes is presented in the paper. More precisely, schemes are tested on one-dimensional linear scalar equation and on non-linear conservation law systems. Furthermore, well-balanced semi-implicit WENO schemes for balance laws with geometrical source terms are defined. Such schemes are then applied to the open channel flow equations. We prove that the defined numerical schemes maintain steady state solution of still water. The application of the new schemes to different open channel flow examples is shown.

Three-dimensional compressible viscous micropolar fluid with cylindrical symmetry: Derivation of the model and a numerical solution

In this paper we consider the nonstationary 3D flow of a compressible viscous and heat-conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The fluid domain is the subset of R3 bounded with two coaxial cylinders that present solid thermoinsulated walls. We assume that the initial mass density, temperature, as well as the velocity and microrotation vectors are radially dependent only. The corresponding solution is also spatially radially dependent. We derive the mathematical model in the Lagrangian description and by using the Faedo–Galerkin method we introduce a system of approximate equations and construct its solutions. We also analyze two numerical examples.

Balanced Central NT Schemes for the Shallow Water Equations

The numerical method we consider is based on the nonstaggered central scheme proposed by Jiang, Levy, Lin, Osher, and Tadmor (SIAM J. Numer. Anal. 35, 2147(1998)) that was obtained by conversion of the standard central NT scheme to the nonstaggered mesh. The generalization we propose is connected with the numerical evaluation of the geometrical source term. The presented scheme is applied to the nonhomogeneous shallow water system. Including an appropriate numerical treatment for the source term evaluation we obtain the scheme that preserves quiescent steady-state for the shallow water equations exactly. We consider two different approaches that depend on the discretization of the riverbed bottom. The obtained schemes are well balanced and present accurate and robust results in both steady and unsteady flow simulations.

GLOBAL SOLUTION TO 1D MODEL OF A COMPRESSIBLE VISCOUS MICROPOLAR HEAT-CONDUCTING FLUID WITH A FREE BOUNDARY

Abstract In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.

Nonconservative Formulation of Unsteady Pipe Flow Model

A new approach to numerical modeling of water hammer is proposed. An unsteady pipe flow model incorporating Brunone’s unsteady friction model is used, but in contrast to the standard treatment of the unsteady friction term as a source term, the writers propose a nonconservative formulation of source term. Second-order flux limited and high order weighted essentially nonoscillating numerical schemes were applied to the proposed formulation, and results are in better agreement with measurements when compared with results obtained with standard form.

Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions

The intention of this work is to concern the numerical solutions to the model of the nonstationary 1d micropolar compressible viscous and heat conducting fluid flow that is in the thermodynamical sense perfect and polytropic. The mathematical model consists of four partial differential equations, transformed from the Eulerian to the Lagrangian description, and which are associated with different boundary conditions. By using the finite difference scheme and the Faedo-Galerkin method we make different numerical simulations to the results of our problems. The properties of both numerical schemes are analyzed and numerical results are compared on the chosen test examples. The comparison of the numerical results on problems that have the homogeneous or the non-homogeneous boundary conditions for velocity and microrotation show good agreement of both approaches. However, the advantage of the used finite difference method over the Faedo-Galerkin method lies in the simple implementation of the non-homogeneous boundary conditions and in the possibility of approximation of the free boundary problem on which the Faedo-Galerkin method is not applicable.

Numerical Simulations of Water Wave Propagation and Flooding

In this paper we present main points in the process of application of numerical schemes for hyperbolic balance laws to water wave propagation and flooding. The appropriate mathematical models are the one-dimensional open channel flow equations and the two-dimensional shallow water equations. Therefore good simulation results can only be obtained with well-balanced numerical schemes such as the ones developed by Bermudez and Vazquez, Hubbard and Garcia-Navarro, LeVeque, etc. as well as the ones developed by the authors of this paper. We also propose a modification of the well-balanced Q-scheme for the two-dimensional shallow water equations that solves the wetting and drying problem. Finally, we present numerical results for three simulation tasks: the CADAM dam break experiment, the water wave propagation in the Toce river, and the catastrophic dam break on the Malpasset river.

Upwind numerical approximations of a compressible 1d micropolar fluid flow

In this paper we consider the numerical approximations of the nonstationary 1D flow of a compressible micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The flow equations are considered in the Eulerian formulation. It is proved that the inviscid micropolar flow equations are hyperbolic and the corresponding eigensystem is determined. The numerical approximations are based on the upwind Roe solver applied to the inviscid part of the flux, while the viscous part of the flux is approximated by using central differences. Numerical results for the inviscid flow show that the numerical schemes approximate the solutions very accurately. The numerical tests for the viscous and heat-conducting flow are also performed.