We calibrate the k-$\omega$$SST$ turbulence model for free surface flows in the channel or on the slope using machine learning techniques. To calibrate the turbulence model, an experiment is carried out in an inclined rectangular research chute. In the experiment, the pressure values in the flow are measured at different distances from the bottom; after transforming data, the flow velocity profile is obtained. The k-$\omega$$SST$ turbulence model is calibrated based on experimental data using the Nelder-Mead optimization algorithm. The calibrated turbulence model is then used to calculate the glacial lake Maliy Azau outburst flood on the Elbrus (Central Caucasus).

The paper considers the slope flow simulation and the problem of finding the optimal parameter values of this mathematical model. The slope flow is modeled using the finite volume method applied to the Reynolds-averaged Navier–Stokes equations with closure in the form of the $k-\omega SST$ turbulence model. The optimal values of the turbulence model coefficients for free surface gravity multiphase flows were found using the global search algorithm. Calibration was performed to increase the similarity of the experimental and calculated velocity profiles. The Root Mean Square Error (RMSE) of derivation between the calculated flow velocity profile and the experimental one is considered as the objective function in the optimization problem. The calibration of the turbulence model coefficients for calculating the free surface flows on test slopes using the multiphase model for interphase tracking has not been performed previously. To solve the multi-extremal optimization problem arising from the search for the minimum of the loss function for the flow velocity profile, we apply a new optimization approach using a Peano curve to reduce the dimensionality of the problem. To speed up the optimization procedure, the objective function was approximated using an artificial neural network. Thus, an interdisciplinary approach was applied which allowed the optimal values of six turbulence model parameters to be found using OpenFOAM and Globalizer software.

The use of default coefficient values in Reynolds-averaged Navier–Stokes turbulence models often yields incorrect results because these coefficients are based on a limited flow types. To solve this problem, a method of calibration and selection of turbulence model input coefficients is proposed using the case of incompressible round jet flow in the range of Reynolds numbers from 5100 to 86 000. For the first time for round jets, the turbulence model is calibrated based on centerline velocity using all input constants. The influence of the coefficients on the axial jet velocity is analyzed. The optimal k−ε turbulence model coefficients are determined for a set of different Reynolds numbers so that the computational result matches the experimental data. Based on these data, the dependencies of the turbulence model coefficients on the Reynolds number are constructed. As a result, an improved k−ε turbulence model based on the open-source software OpenFOAM is implemented using these relations. The main advantage of the proposed model is its dependence on a single input parameter—the Reynolds number, which is based on the nozzle exit diameter. Other coefficients are determined as a function of the Reynolds number. A validation of the improved model on jet flows at other Reynolds numbers, which are not involved in the calibration process, is performed. It is found that the proposed model significantly refines the solution for incompressible jets both in the near and far field, which allows its use in other applied applications.

The work is devoted to the comparison of different approaches for modeling the dynamics of dense and powder snow avalanches. Various 3D and 2D approaches are considered. The accuracy of determining the avalanche run-out zone, the interaction of the flow with obstacles, the front speed, and various distributed parameters are evaluated. As objects for comparison, an experiment on the interaction of a slushflow with a combination of protective structures and a powder snow avalanche in the Khibiny mountains are modeled. Taking into account the advantages and disadvantages of various approaches based on basic solutions available in the OpenFOAM package, a specialized software avalancheFoam is being developed for three-dimensional modeling of the dynamics of snow avalanches, taking into account the complex turbulent regime and multiphase structure of the flow. Machine learning techniques are used to refine turbulent stresses. The neural network is trained on a dataset obtained from high-precision supercomputer simulation of the flow, and sets the form of additional refinement members of the mathematical model of less computational complexity. Various avalanche sites in the Khibiny mountains are modeled to validate the developed software.

Some numerical results obtained by modeling the thermogas displacement of oil from a porous reservoir are discussed. The displacement is performed by a heated water-gas mixture. The injected...

В работе проводится калибровка k − ε модели турбулентности для потоков со свободной поверхностью в русле и на склоне. Для калибровки модели проводится эксперимент в наклонном лотке постоянного уклона прямоугольного сечения. В эксперименте с помощью трубки Пито измеряются значения давления в потоке на различном расстоянии от дна, с помощью которых так же получается профиль скорости потока. На основании данных эксперимента с использованием алгоритма оптимизации Нелдера-Мида производится калибровка k − ε модели турбулентности. Откалиброванная модель турбулентности далее применяется для расчёта прорыва ледникового озера, вблизи ледника Малый Азау.