Geodesic
Numerical study of hydrodynamics of underwater missile launch
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 1, pp. 65-75

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A mathematical model and a calculation method for hydrodynamics of a missile take-off from a submerged silo of a submarine are offered. A non-axisymmetric flow area in the mine is transformed into an axisymmetric one by a conform mapping, and a 3D boundary value problem is reduced to a series of axisymmetric problems that are solved by Galerkin's method with using the method of finite elements. A nonstationary interaction between a liquid filling the silo and a missile loaded in it is expressed through dependencies of apparent mass on the following geometry parameters of the silo and the missile: a width of a circumferential gap, the missile shape, and a location of the gas–liquid interface. The provided calculation algorithm of the apparent mass is implemented as a computer program. The resulted verification of the numerical simulation with data of analytical solutions confirms sufficient fidelity of the developed mathematical model of the missile hydrodynamics in the restricted liquid volume.
Keywords: missile, take-off, hydrodynamics, apparent mass, conformal transformation, method of finite elements. 
@article{CHFMJ_2019_4_1_a5,
     author = {V. I. Pegov},
     title = {Numerical study of hydrodynamics of underwater missile launch},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {65--75},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_1_a5/}
}
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V. I. Pegov. Numerical study of hydrodynamics of underwater missile launch. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 1, pp. 65-75. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_1_a5/