and Computational Methods

#### 532.51 Multiscale modeling of liquid binder filtration processes in composite structures manufactured by RTM

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Bogdanov I. O. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-327

A mathematical model for the multiscale process of filtration of weakly compressible liquids and gases in periodic porous media is proposed with reference to the process of composite material production based on the RTM method. Using the method of asymptotic averaging made it possible to formulate the so-called local filtration problems for a single pore and the global problem of unsteady filtration of weakly compressible liquids. Two models of a weakly compressible fluid are considered: classical and generalized. The classical model is based on the Musket’s equation of the state, which requires initial constant values for fluid pressure and density to be preset. The generalized model is based on the same equation, but requires presetting only the initial fluid density, using the unknown hydrostatic pressure instead of the initial constant liquid pressure. The results of simulation of the impregnation process of a of filler material sample by a binder are presented using the two models of a weakly compressible liquid.

Dimitrienko Yu. I.Bogdanov I.O. Multiscale modeling of liquid binder filtration processes in composite structures manufactured by RTM Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 3-27

#### 62-752 Modeling loads on compound elastic shells by means of the initial approximation method

**Dubrovin V. M. (Bauman Moscow State Technical University), Butina T. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-2838

The article presents a method for computing loads (such as strain or torque) on a compound shell consisting of elastically linked external and internal shells for the case when the external shell is subjected to transverse loading (bending moment, shear forces and distributed inertial loads). To demonstrate the application of our method, we investigated the effect the rigidity properties of the external shell have on the internal shell loading.

Dubrovin V.M., Butina T.A. Modeling loads on compound elastic shells by means of the initial approximation method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 28-38

#### 629.762 Mathematical simulation of the process of water entering the annular space of a canister during submarine gas-driven aircraft ejection

**Plyusnin A. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-3964

The study deals with a one-dimensional analytical model for computing the loads on the body of an aircraft caused by water entering the annular space of a launch canister. We used potential theory to solve the "external" hydrodynamic problem. Solving Lamé equations for the static case accounts for the strain in the walls of the aircraft and the launch canister.

Plyusnin A.V. Mathematical simulation of the process of water entering the annular space of a canister during submarine gas-driven aircraft ejection. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 39-64

#### 533.16 Techniques for numerical simulation flow around an axisymmetric blunt body in an underexpanded jet of liquid rocket engine combustion products

**Gorskiy V. V. (Bauman Moscow State Technical University), Kovalsky M. G.**

doi: 10.18698/2309-3684-2017-2-6580

Testing thermal protection in jets of propulsion system combustion products is one of the priority types of its experimental development. The informational content of such trials depends to a large extent on the mathematical modeling of the processes taking place in the experiments under consideration. They include flow past a model made of ablative thermal protection, convective heat transfer and friction in the laminar-turbulent boundary layer formed on the model surface, ablation of thermal protection and change in the shape of the model. The article describes the mathematical modeling of the first of the above processes, associated with solving the complex problem of constructing the field of gas dynamic functions in the underexpanded high-pressure jet of the liquid rocket engine combustion products in a flooded space and the divergent jet flow around the model surface. The results of comparison of analytical results with experimental data are presented.

V.V. Gorsky, M.G. Kovalsky Techniques for numerical simulation flow around an axisymmetric blunt body in an underexpanded jet of liquid rocket engine combustion products. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 65-80

#### 533.6.011.5 Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid

**Bulgakov V. N. (Bauman Moscow State Technical University), Kotenev V. P. (Bauman Moscow State Technical University), Sapozhnikov D. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-8193

The article presents an analytical expression for calculating pressure on the surface of blunted cones in a supersonic gas flow, taking into account the curvature discontinuity along the generatrix. We used a genetic algorithm and multi-stage functional optimisation methods for the least-squares method to determine free parameters of the expression. We compare the results obtained to the rigorous numerical solution to the inviscid problem. The comparison shows that it is possible to use the analytical expression for pressure distribution over a surface in a wide Mach number range for various cone halfangles. The expression proposed accounts for the curvature discontinuity along the generatrix at the point where the sphere is tangent to the conical surface, unlike the expressions found in previously published works.

Bulgakov V.N., Kotenev V.P., Sapozhnikov D.A. Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 81-93

#### 519.6 Numerical solution to problems of optimal control with switching by means of the shooting method

**Mozzhorina T. Y. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-94106

We conducted a numerical experiment in applying the shooting method to solve problems of optimal control with switching. We used the problem of lunar soft-landing to test an algorithm that ensures convergence of Newton's method in problems of this type. We analysed the accuracy of our computations.

Mozzhorina T. Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 94-106

#### 519.8 “Mixed” stochastic models of reciprocal hostilities for the case of one belligerent performing a pre-emptive strike

**Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-2-107123

We used the theory of continuous-time Markov processes as the basis for developing our stochastic “mixed” models of reciprocal hostilities and a numerical algorithm that makes it possible to compute main combat metrics for large forces. We show that a pre-emptive strike performed by one of the belligerents significantly affects the outcome and main metrics of combat between forces that are sufficiently similar in strength. We determine that it is not the initial numerical strengths of the two belligerents but their balance of power that affects errors shown by the method of dynamics of mean values; moreover, the errors increase with increasing the time to a pre-emptive strike.

Chuev V. Yu., Dubogray I.V. “Mixed” stochastic models of reciprocal hostilities for the case of one belligerent performing a pre-emptive strike. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 107-123