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In present paper we reexamine the properties of CABARET numerical scheme formulated for a weakly compressible fluid flow basing the results of free shear layer modeling. Kelvin–Helmholtz instability and successive generation of two-dimensional turbulence provide a wide field for a scheme analysis including temporal evolution of the integral energy and enstrophy curves, the vorticity patterns and energy spectra, as well as the dispersion relation for the instability increment. The most part of calculations is performed for Reynolds number $\text{Re} = 4 \times 10^5$ for square grids sequentially refined in the range of $128^2-2048^2$ nodes. An attention is paid to the problem of underresolved layers generating a spurious vortex during the vorticity layers roll-up. This phenomenon takes place only on a coarse grid with $128^2$ nodes, while the fully regularized evolution pattern of vorticity appears only when approaching $1024^2$-node grid. We also discuss the vorticity resolution properties of grids used with respect to dimensional estimates for the eddies at the borders of the inertial interval, showing that the available range of grids appears to be sufficient for a good resolution of small–scale vorticity patches. Nevertheless, we claim for the convergence achieved for the domains occupied by large-scale structures.

The generated turbulence evolution is consistent with theoretical concepts imposing the emergence of large vortices, which collect all the kinetic energy of motion, and solitary small-scale eddies. The latter resemble the coherent structures surviving in the filamentation process and almost noninteracting with other scales. The dissipative characteristics of numerical method employed are discussed in terms of kinetic energy dissipation rate calculated directly and basing theoretical laws for incompressible (via enstrophy curves) and compressible (with respect to the strain rate tensor and dilatation) fluid models. The asymptotic behavior of the kinetic energy and enstrophy cascades comply with two-dimensional turbulence laws $E(k) \propto k^{−3}, \omega^2(k) \propto k^{−1}$. Considering the instability increment as a function of dimensionless wave number shows a good agreement with other papers, however, commonly used method of instability growth rate calculation is not always accurate, so some modification is proposed. Thus, the implemented CABARET scheme possessing remarkably small numerical dissipation and good vorticity resolution is quite competitive approach compared to other high-order accuracy methods

When a supersonic air flow interacts with a transverse secondary jet injected into this flow through an orifice on a flat wall, a special flow structure is formed. This flow takes place during fuel injection into combustion chambers of supersonic aircraft engines; therefore, in recent years, various approaches to intensifying gas mixing in this type of flow have been proposed and studied in several countries. The approach proposed in this work implies using spark discharges for pulsed heating of the gas and generating the instabilities in the shear layer at the boundary of the secondary jet. Using simulation in the software package FlowVision 3.13, the characteristics of this flow were obtained in the absence and presence of pulsed-periodic local heat release on the wall on the windward side of the injector opening. A comparison was made of local characteristics at different periodicities of pulsed heating (corresponding to the values of the Strouhal number 0.25 and 0.31). It is shown that pulsed heating can stimulate the formation of perturbations in the shear layer at the jet boundary. For the case of the absence of heating and for two modes of pulsed heating, the values of an integral criterion for mixing efficiency were calculated. It is shown that pulsed heating can lead both to a decrease in the average mixing efficiency and to its increase (up to 9% in the considered heating mode). The calculation method used (unsteady Reynolds-averaged Navier – Stokes equations with a modified $k-\varepsilon$ turbulence model) was validated by considering a typical case of the secondary transverse jet interaction with a supersonic flow, which was studied by several independent research groups and well documented in the literature. The grid convergence was shown for the simulation of this typical case in FlowVision. A quantitative comparison was made of the results obtained from FlowVision calculations with experimental data and calculations in other programs. The results of this study can be useful for specialists dealing with the problems of gas mixing and combustion in a supersonic flow, as well as the development of engines for supersonic aviation.

In this paper a numerical model for blood flow through a venous bifurcation with an obliterating clot is investigated. We studied propagation of perturbations of blood flow velocity and perturbations of pressure inside the vein. The model is built in acoustic (linear) approximation. Computational results reveal conditions for clot resonance oscillation, which can cause its detachment and thromboembolism.

The problem discrete statement by the smoothed particle hydrodynamics method (SPH) include a discretization constants parameters set. Of them particular note is the model sound speed $c_0$, which relates the SPH-particle instantaneous density to the resulting pressure through the equation of state.

The paper describes an approach to the exact determination of the model sound speed required value. It is on the analysis based, how SPH-particle density changes with their relative shift. An example of the continuous medium motion taken the plane shear flow problem; the analysis object is the relative compaction function $\varepsilon_\rho$ in the SPH-particle. For various smoothing kernels was research the functions of $\varepsilon_\rho$, that allowed the pulsating nature of the pressures occurrence in particles to establish. Also the neighbors uniform distribution in the smoothing domain was determined, at which shaping the maximum of compaction in the particle.

Through comparison the function $\varepsilon_\rho$ with the SPH-approximation of motion equation is defined associate the discretization parameter $c_0$ with the smoothing kernel shape and other problem parameters. As a result, an equation is formulated that the necessary and sufficient model sound speed value provides finding. For such equation the expressions of root $c_0$ are given for three different smoothing kernels, that simplified from polynomials to numerical coefficients for the plane shear flow problem parameters.

In this paper on the basis of the riverbed model proposed earlier the one-dimensional stability problem of closed flow channel with sandy bed is solved. The feature of the investigated problem is used original equation of riverbed deformations, which takes into account the influence of mechanical and granulometric bed material characteristics and the bed slope when riverbed analyzing. Another feature of the discussed problem is the consideration together with shear stress influence normal stress influence when investigating the riverbed instability. The analytical dependence determined the wave length of fast-growing bed perturbations is obtained from the solution of the sandy bed stability problem for closed flow channel. The analysis of the obtained analytical dependence is performed. It is shown that the obtained dependence generalizes the row of well-known empirical formulas: Coleman, Shulyak and Bagnold. The structure of the obtained analytical dependence denotes the existence of two hydrodynamic regimes characterized by the Froude number, at which the bed perturbations growth can strongly or weakly depend on the Froude number. Considering a natural stochasticity of the waves movement process and the presence of a definition domain of the solution with a weak dependence on the Froude numbers it can be concluded that the experimental observation of the of the bed waves movement development should lead to the data acquisition with a significant dispersion and it occurs in reality.

The work is a theoretical study of the development of bottom instability in rivers and canals. Based on an analytical model of the load of sediment, taking into account the influence of slopes of the bottom surface, bottom pressure and shear stress on the movement of the bottom material and an analytical solution that allows to determine bottom tangential and normal stresses over the periodic bottom, the problem of determining the amplitude growth rate for growing bottom waves is formulated and solved . The obtained solution of the problem allows us to determine the characteristic time of the growth of the bottom wave, the growth rate of the bottom wave and its maximum amplitude, depending on the physical and particle size characteristics of the bottom material and the hydraulic parameters of the water flow. On the example of the development of a periodic sinusoidal bottom wave of low steepness, the verification of the solution obtained for the formulated problem is carried out. The obtained analytical solution to the problem allows us to determine the growth rate of the amplitude of the bottom wave from the current value of its amplitude. Comparison of the obtained solution with experimental data showed their good qualitative and quantitative agreement.

The paper considers models of platelet thrombus formation in blood plasma flow in a cylindrical vessel, based on the “advection–diffusion” equation and the Fokker–Planck equation. The comparison of the results of calculations based on these models is given. Considered models show qualitatively similar behavior at the initial stage of thrombus formation. А detailed investigation of large clots requires models’ improvement.

Atherosclerotic diseases such as carotid artery diseases (CAD) and chronic kidney diseases (CKD) are the major causes of death worldwide. The onset of these atherosclerotic diseases in the arteries are governed by complex blood flow dynamics and hemodynamic parameters. Atherosclerosis in renal arteries leads to reduction in arterial efficiency, which ultimately leads to Reno-vascular hypertension. This work attempts to identify the localization of atherosclerotic plaque in human abdominal aorta — renal artery junction using Computational fluid dynamics (CFD).

The atherosclerosis prone regions in an idealized human abdominal aorta-renal artery junction are identified by calculating relevant hemodynamic indicators from computational simulations using the rheologically accurate shear-thinning Yeleswarapu model for human blood. Blood flow is numerically simulated in a 3-D model of the artery junction using ANSYS FLUENT v18.2.

Hemodynamic indicators calculated are average wall shear stress (AWSS), oscillatory shear index (OSI), and relative residence time (RRT). Simulations of pulsatile flow (f=1.25 Hz, Re = 1000) show that low AWSS, and high OSI manifest in the regions of renal artery downstream of the junction and on the infrarenal section of the abdominal aorta lateral to the junction. High RRT, which is a relative index and dependent on AWSS and OSI, is found to overlap with the low AWSS and high OSI at the cranial surface of renal artery proximal to the junction and on the surface of the abdominal aorta lateral to the bifurcation: this indicates that these regions of the junction are prone to atherosclerosis. The results match qualitatively with the findings reported in literature and serve as initial step to illustrate utility of CFD for the location of atherosclerotic plaque.

The mechanisms of hydrodynamical activation of blood coagulation system are investigated in stenosed vessels for a wide range of Reynolds number values (from 10 up to 500). It is assumed that the vessel wall permeability for procoagulant factors rapidly increases when wall shear stress exceeds specific threshold value. A number of patterns of blood coagulation processes development are described. The influence of blood flow topology changes on activation of blood coagulation is explored. It is established that not only blood flow decrease, but also its increase may promote activation of blood coagulation. It was found that dependence of thrombogenic danger of stenosis on vessel lumen blockage ratio is non-monotonic. The relevance of obtained theoretical results for clinical practice is discussed.

Numerical modeling of shear-induced platelet activation in haemodialysis arteriovenous fistulas was carried out in this work. The goal was to investigate the mechanisms of threshold shear-induced platelet activation in fistulas. For shear-induced platelet activation to take place, shear stress accumulated by platelets along corresponding trajectories in blood flow had to exceed a definite threshold value. The threshold value of cumulative shear stress was supposed to depend on the multimer size of von Willebrand factor macromolecules acting as hydrodynamic sensors for platelets. The effect of arteriovenous fistulas parameters, such as the anastomotic angle, blood flow rate, and the multimer size of von Willebrand factor macromolecules, on platelet activation risk was studied. Parametric diagrams have been constructed that make it possible to distinguish the areas of parameters corresponding to the presence or absence of shear-induced platelet activation. Scaling relations that approximate critical curves on parametric diagrams were obtained. Analysis showed that threshold fistula flow rate is higher for obtuse anastomotic angle than for sharp ones. This means that a fistula with obtuse angle can be used in wider flow rate range without risk of platelet activation. In addition, a study of different anastomosis configurations of arteriovenous fistulas showed that the configuration “end of vein to end of artery” is among the safest. For all the investigated anastomosis configurations, the critical curves on the parametric diagrams were monotonically decreasing functions of von Willebrand factor multimer size. It was shown that fistula flow rate should have a significant impact on the probability of thrombus formation initiation, while the direction of flow through the distal artery did not affect platelet activation. The obtained results allowed to determine the safest fistula configurations with respect to thrombus formation triggering. The authors believe that the results of the work may be of interest to doctors performing surgical operations for creation of arteriovenous fistulas for haemodialysis. In the final section of the work, possible clinical applications of the obtained results by means of mathematical modeling are discussed.