Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.

Simulation of Dam Breaks on Dry Bed Using Finite Volume Roe-TVD Method

Dams are one of the most important hydraulic structures. In view of unrecoverable damages occurring after a dam failure, analyzing a dams’ break is necessary. In this study, a dam located in Iran is considered. According to adjacent tourist and entertainment zones, the breaking of the dam could lead to severe problems for the area and bridges downstream of the river. To investigate the issue, a numerical FORTRAN code based on the 2D finite volume Roe-TVD method on a fixed bed is provided to assess the effects of the dam break. Turbulence terms and dry bed conditions were considered in the code. A numerical wave tank (NWT) with a triangular barrier in the bed was numerically modeled and compared with analytical models to verify the capability of the code. Comparing numerical, experimental and analytical results showed that estimated water level and mass conservation in the numerical model is in good agreement with the experimental data and analytical solutions. The 2D approach used has reduced the cost of computing compared to a 3D approach while obtaining accurate results. The code is finally applied to a full-scale dam-break flood. Six KM of the natural river downstream of the dam, including two bridges, B1 and B2, is considered. Flood flow hydrographs and water level variations at bridges B1 and B2 are presented. The results denoted that bridges B1 and B2 will be flooded after 12 and 21 min, respectively, and are at risk of the potential break. Thus, it is necessary to announce and possibly evacuate the resort area alongside the dam in order to decrease losses.

Heat-mass transfer simulation of fluid media in the magma channel

<p>The paper presents a non-stationary model of heat-mass transfer of heterophase media in application to the study of the intrusion processes of magmatic melts in permeable zones of the lithospheric mantle and crust. Special emphasis is given to the study of the change in rheological properties of the fluido-magmatic mixture in the process of magmatic channel formation. The increased compressibility of the fluid phase is taken into account in the model by setting the Van der Waals equation of state. The calculated values of thermodynamic parameters of the fluid-magmatic system such as pressure, temperature, volumetric phase content, are the basis for the analysis of metasomatic changes in mantle matter. The Numerical model is based on the Runge-Kutta-TVD method. Verification of the numerical model on standard tests shows good accuracy of the program code and the possibility of using it for investigations of the currents of fluid-magmatic flows. The study of variation in interphase interaction parameters during melt movement in permeable zone, including change in interphase viscous friction, demonstrates a significant change in temperature distribution in the section of fluid-magmatic system. The work was financially supported by the Russian Foundation for Basic Research, grants No. 19-05-00788.</p>