Numerical modeling of the 2013 meteorite entry in Lake Chebarkul, Russia

The results of the numerical simulation of possible hydrodynamic perturbations in Lake Chebarkul (Russia) as a consequence of the meteorite fall of 2013 (15 February) are presented. The numerical modeling is based on the Navier–Stokes equations for a two-phase fluid. The results of the simulation of a meteorite entering the water at an angle of 20° are given. Numerical experiments are carried out both when the lake is covered with ice and when it is not. The estimation of size of the destructed ice cover is made. It is shown that the size of the observed ice hole at the place of the meteorite fall is in good agreement with the theoretical predictions, as well as with other estimates. The heights of tsunami waves generated by a small meteorite entering the lake are small enough (a few centimeters) according to the estimations. However, the danger of a tsunami of meteorite or asteroid origin should not be underestimated

Three-dimensional numerical simulation of tsunami waves based on the navier-stokes equations

A numerical algorithm of solving the three-dimensional system of Navier-Stokes equations to simulate free surface waves and flows with gravity is presented. The main problem here is to ensure that the gravity force is properly accounted in the presence of discontinuities in the medium density. The task is made more complicated due the use of unstructured computational grids with collocated placement of unknown quantities and splitting algorithms based on SIMPLE-type methods. To obtain correctly the hydrostatic pressure, it is suggested that the contribution of the gravitational force in the equation for pressure should be distinguished explicitly; the latter being calculated by using the solution of the two-phase medium gravitational balance problem. To ensure the balance of the gravity force and the pressure gradient in the case of rest an algorithm in which the pressure gradient in the equation of motion is replaced by a modification considering the gravitational force action is suggested. This method is demonstrated by the example of tsunami wave propagation in the real water area of the World Ocean. © 2017 - TSUNAMI SOCIETY INTERNATIONAL

Tsunamis in the Black Sea: Comparison of the historical, instrumental, and numerical data

The tsunami hazard in the Black Sea is discussed by comparing historical, instrumental data and numerical results. There are 22 tsunami events in the Black Sea documented since the first century, and nine of them have occurred in twentieth century. The numerical simulations of tsunami propagation for the 1966 and 1939 events are performed by using the framework of the shallow-water theory. The instrumental data from tide gauge records are used to compare and validate the simulation results and estimate the wave motion at other locations where the instrumental data are unavailable. The distribution of maximum positive tsunami amplitudes along the north and south coasts are obtained for each event. The arrival time, tsunami amplitudes, and directivity of tsunamis in the Black Sea are studied. The probable source and target areas of tsunamis are discussed

Automatic control of rotary pump using measurements of oil-well liquid by on-line proton magnetic resonance analyzer

In the paper described system of automotive control of installation of rotary pump of oil-mining using parameters of oil-well liquid, measured by on-line proton magnetic resonance analyzer. Described theoretical basis of the system and its practical use. Mathematically modeled system tooling tuning) at changing moment of strength from features of oil-well liquid

Implementation of Flux Limiters in Simulation of External Aerodynamic Problems on Unstructured Meshes

The study is dedicated to the peculiarities of implementing the flux limiter of the flow quantity gradient when solving 3D aerodynamic problems using the system of Navier–Stokes equations on unstructured meshes. The paper describes discretisation of the system of Navier–Stokes equations on a finite-volume method and a mathematical model including Spalart–Allmaras turbulence model and the Advection Upstream Splitting Method (AUSM+) computational scheme for convective fluxes that use a second-order approximation scheme for reconstruction of the solution on a facet. A solution of problems with shock wave structures is considered, where, to prevent oscillations at discontinuous solutions, the order of accuracy is reduced due to the implementation of the limiter function of the gradient. In particular, the Venkatakrishnan limiter was chosen. The study analyses this limiter as it impacts the accuracy of the results and monotonicity of the solution. It is shown that, when the limiter is used in a classical formulation, when the operation threshold is based on the characteristic size of the cell of the mesh, it facilitates suppression of non-physical oscillations in the solution and the upgrade of its monotonicity. However, when computing on unstructured meshes, the Venkatakrishnan limiter in this setup can result in the occurrence of the areas of its accidental activation, and that influences the accuracy of the produced result. The Venkatakrishnan limiter is proposed for unstructured meshes, where the formulation of the operation threshold is proposed based on the gas dynamics parameters of the flow. The proposed option of the function is characterized by the absence of parasite regions of accidental activation and ensures its operation only in the region of high gradients. Monotonicity properties, as compared to the classical formulation, are preserved. Constants of operation thresholds are compared for both options using the example of numerical solution of the problem with shock wave processes on different meshes. Recommendations regarding optimum values of these quantities are provided. Problems with a supersonic flow in a channel with a wedge and transonic flow over NACA0012 airfoil were selected for the examination of the limiter functions applicability. The computation was carried out using unstructured meshes consisting of tetrahedrons, truncated hexahedrons, and polyhedrons. The region of accidental activation of the Venkatakrishnan limiter in a classical formulation, and the absence of such regions in case a modified option of the limiter function, is implemented. The analysis of the flow field around a NACA0012 indicates that the proposed improved implementation of the Venkatakrishnan limiter enables an increase in the accuracy of the solution