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The influence of the process of initiating a rapid local heat release near surface streamlined by supersonic gas (air) flow on the separation region that occurs during a fast turn of the flow was investigated. This surface consists of two planes that form obtuse angle when crossing, so that when flowing around the formed surface, the supersonic gas flow turns by a positive angle, which forms an oblique shock wave that interacts with the boundary layer and causes flow separation. Rapid local heating of the gas above the streamlined surface simulates long spark discharge of submicrosecond duration that crosses the flow. The gas heated in the discharge zone interacts with the separation region. The flow can be considered two-dimensional, so the numerical simulation is carried out in a two-dimensional formulation. Numerical simulation was carried out for laminar regime of flow using the sonicFoam solver of the OpenFOAM software package.

The paper describes a method for constructing a two-dimensional computational grid using hexagonal cells. A study of grid convergence has been carried out. A technique is given for setting the initial profiles of the flow parameters at the entrance to the computational domain, which makes it possible to reduce the computation time by reducing the number of computational cells. A method for non-stationary simulation of the process of rapid local heating of a gas is described, which consists in superimposing additional fields of increased pressure and temperature values calculated from the amount of energy deposited in oncoming supersonic gas flow on the corresponding fields of values obtained in the stationary case. The parameters of the energy input into the flow corresponding to the parameters of the electric discharge process, as well as the parameters of the oncoming flow, are close to the experimental values.

During analyzing numerical simulation data it was found that the initiation of rapid local heating leads to the appearance of a gas-dynamic perturbation (a quasi-cylindrical shock wave and an unsteady swirling flow), which, when interacting with the separation region, leads to a displacement of the separation point downstream. The paper considers the question of the influence of the energy spent on local heating of the gas, and of the position on the streamlined surface of the place of heating relative to the separation point, on the value of its maximum displacement.

The possibility of numerical 3D simulation of thrombi formation is considered.

The developed up to now detailed mathematical models describing formation of thrombi and clots include a great number of equations. Being implemented in a CFD code, the detailed mathematical models require essential computer resources for simulation of the thrombi growth in a blood flow. A reasonable alternative way is using reduced mathematical models. Two models based on the reduced mathematical model for the thrombin generation are described in the given paper.

The first model describes growth of a thrombus in a great vessel (artery). The artery flows are essentially unsteady. They are characterized by pulse waves. The blood velocity here is high compared to that in the vein tree. The reduced model for the thrombin generation and the thrombus growth in an artery is relatively simple. The processes accompanying the thrombin generation in arteries are well described by the zero-order approximation.

A vein flow is characterized lower velocity value, lower gradients, and lower shear stresses. In order to simulate the thrombin generation in veins, a more complex system of equations has to be solved. The model must allow for all the non-linear terms in the right-hand sides of the equations.

The simulation is carried out in the industrial software FlowVision.

The performed numerical investigations have shown the suitability of the reduced models for simulation of thrombin generation and thrombus growth. The calculations demonstrate formation of the recirculation zone behind a thrombus. The concentration of thrombin and the mass fraction of activated platelets are maximum here. Formation of such a zone causes slow growth of the thrombus downstream. At the upwind part of the thrombus, the concentration of activated platelets is low, and the upstream thrombus growth is negligible.

When the blood flow variation during a hart cycle is taken into account, the thrombus growth proceeds substantially slower compared to the results obtained under the assumption of constant (averaged over a hard cycle) conditions. Thrombin and activated platelets produced during diastole are quickly carried away by the blood flow during systole. Account of non-Newtonian rheology of blood noticeably affects the results.