Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.

Parallel algorithms for solving diffusion-convection problems on a multiprocessor computer system using hybrid MPI / OpenMP technology

The paper deals with the mathematical models, algorithms and software for mathematical modeling of coastal systems’ water pollution spreading dynamics under various unfavorable phenomena of natural and artificial genesis, developed for high-performance cluster systems. Methods for partitioning the computational domain for solving diffusion-convection problems have been developed, which allow for efficient parallelization of a computationally complex modeling problem, taking into account the architecture of the multiprocessor system used. The developed mathematical models are based on high-precision models of hydrophysics and hydrobiology and take into account the peculiarities of water systems in the south of the Rostov region, as well as factors of hydrobiological dynamics such as microturbulent diffusion and advective transport in various directions, mechanisms of primary and secondary pollution of coastal systems, taking into account currents. The paper presents algorithms for solving a simulated problem based on MPI parallelization technology, as well as based on mixed MPI + OpenMP technology. Numerical experiments have been carried out and the two technologies efficiency comparison has been made in the conditions of computing cluster used.

Mathematical Modeling of the Phytoplankton Populations Geographic Dynamics for Possible Scenarios of Changes in the Azov Sea Hydrological Regime

Increased influence of abiotic and anthropogenic factors on the ecological state of coastal systems leads to uncontrollable changes in the overall ecosystem. This paper considers the crucial problem of studying the effect of an increase in the water’s salinity in the Azov Sea and the Taganrog Bay on hydrobiological processes. The main aim of the research is the diagnostic and predictive modeling of the geographic dynamics of the general phytoplankton populations. A mathematical model that describes the dynamics of three types of phytoplankton is proposed, considering the influence of salinity and nutrients on algae development. Discretization is carried out based on a linear combination of Upwind Leapfrog difference schemes and a central difference scheme, which makes it possible to increase the accuracy of solving the biological kinetics problem at large values of the grid Péclet number (Peh > 2). A software package has been developed that implements interrelated models of hydrodynamics and biogeochemical cycles. A modified alternating-triangular method was used to solve large-dimensional systems of linear algebraic equations (SLAE). Based on the scenario approach, several numerical experiments were carried out to simulate the dynamics of the main species of phytoplankton populations at different levels of water salinity in coastal systems. It is shown that with an increase in the salinity of waters, the habitats of phytoplankton populations shift, and marine species invasively replace freshwater species of algae.

An Integrated, Probabilistic Modeling Approach to Assess the Evolution of Barrier-Island Systems Over the Twenty-First Century

Barrier-island systems, spanning ∼7% of the world’s coastlines, are of great importance to society because not only they provide attractive, liveable space for coastal communities but also act as the first line of defense from coastal storms. As many of these unique coastal systems are affected by both oceanic and terrestrial processes, it is necessary to consider the holistic behavior of applicable terrestrial and coastal processes when investigating their evolution under plausible future scenarios for climate change, population growth and human activities. Such holistic assessments, also accounting for uncertainties, can readily be achieved via reduced-complexity modeling techniques, owing to their much faster simulation times compared to sophisticated process-based models. Here, we develop and demonstrate a novel probabilistic modeling framework to obtain stochastic projections of barrier-island evolution over the twenty-first century while accounting for relevant oceanic and terrestrial processes under climate change impacts and anthropogenic activities. The model is here demonstrated at the Chandeleur islands (Louisiana, United States) under the four Intergovernmental Panel on Climate Change (IPCC) greenhouse gas emission scenarios (i.e., Representative Concentration Pathways 2.6, 4.5, 6.0, and 8.5) with results indicating that there are significant uncertainties in projected end-century barrier-island migration distance and available barrier freeboard under the high emission scenario RCP 8.5. The range of uncertainties in these projections underscores the value of stochastic projections in supporting the development of effective adaptation strategies for these fragile coastal systems.

Evaluation of the Potential Release Tendency of Metals and Metalloids from the Estuarine Sediments: Case Study of Raša Bay

Assessing the environmental quality of coastal systems is important not only for the management and protection of such areas, but also for improving the quality of water resources. Since sediment itself can often be a source of certain toxic elements, in addition to information on the distribution of metals in the water column and in the sediment itself, it is useful to determine the bioavailable forms of individual elements, particularly toxic ones. In this study, water and sediment geochemical data were supplemented with oxyanion mobility in sediments estimated by diffusion gradients in thin film (DGTs). The data obtained indicate that the chemical composition of the water in the Raša River estuary primarily reflects the high input of suspended sediment from the catchment, the mixing of freshwater and seawater, and to a lesser extent the effects of anthropogenic activities. Although sediment composition is primarily determined by geological and hydrodynamic conditions in the catchment, it also indicates moderate enrichment in Co, Cr, Mo and Ni. In contrast, the distribution of oxyanions in sediment pore water indicates the influence of sediment as a source of some elements in the bottom water; e.g., sediment contributes to 40% of the arsenic bottom water budget. The obtained depth profiles of the oxyanion distribution in the sediment pore water indicate an early onset of suboxic to anoxic conditions in Raša Bay, which is prone to rapid sedimentation. All this demonstrates the need to consider the bioavailable forms of elements when assessing environmental quality, as the lack of such information can lead to an incomplete assessment, especially in dynamic coastal systems such as estuaries.