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Mathematical Models and Computer Simulations

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01-06-2023

Test Problems of Gas Suspension Dynamics Using Asymptotically Exact Solutions

Author: D. V. Sadin

Published in: Mathematical Models and Computer Simulations | Issue 3/2023

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Abstract

Asymptotically exact solutions of Riemann problems are constructed under the assumption of small scales of dynamic and thermal relaxations of a gas-dispersed mixture. Depending on the parameters of the gas suspension’s states on different sides of the initial arbitrary discontinuities, configurations with two shock waves, a rarefaction wave and a shock wave, as well as two rarefaction waves are formed. For these benchmarks, the computational properties of the balanced algorithm of a hybrid large-particle method, suitable for solving stiff problems, are tested. The features of nonequilibrium wave flows of a gas suspension and the convergence of numerical solutions to asymptotically exact solutions with decreasing particle size of the gas suspension are studied.

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B. L. Roždestvenskii and N. N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics, 2nd ed. (Nauka, Moscow, 1978; Am. Math. Soc., Providence, RI, 1983).

C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 2: Computational Methods for Inviscid and Viscous Flows (Wiley, New York, 1990).

A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman & Hall/CRC, Boca Raton, FL, 2001).

E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics (Springer, Berlin, 2009).CrossRefMATH

R. I. Nigmatulin, Dynamics of Multiphase Media, Vols. 1, 2 (Nauka, Moscow, 1987; CRC Press, New York, 1990).

G. A. Ruev, B. L. Rozhdestvenskii, V. M. Fomin, and N. N. Yanenko, “Conservation laws for systems of equations for two-phase media,” Sov. Math. Dokl. 22 (2), 352–357 (1980).

L. A. Klebanov, A. E. Kroshilin, B. I. Nigmatulin, R. I. Nigmatulin, “On the hyperbolicity, stability and correctness of the Cauchy problem for the system of equations of two-speed motion of two-phase media,” J. Appl. Math. Mech., 46 (1), 66–74 (1982). https://doi.org/10.1016/0021-8928(82)90084-3MathSciNetCrossRefMATH

R. Abgrall and R. Saurel, “Discrete equations for physical and numerical compressible multiphase mixtures,” J. Comput. Phys. 186 (2), 361–396 (2003). https://doi.org/10.1016/S0021-9991(03)00011-1MathSciNetCrossRefMATH

R. Saurel and R. Abgrall, “A multiphase Godunov method for compressible multifluid and multiphase flows,” J. Comput. Phys. 150 (2), 425–467 (1999). https://doi.org/10.1006/jcph.1999.6187MathSciNetCrossRefMATH

10.

S. A. Tokareva and E. F. Toro, “HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow,” J. Comput. Phys. 229 (10), 3573–3604 (2010). https://doi.org/10.1016/j.jcp.2010.01.016MathSciNetCrossRefMATH

11.

M. Dumbser and D. S. Balsara, “A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems,” J. Comput. Phys. 304, 275–319 (2016). https://doi.org/10.1016/j.jcp.2015.10.014MathSciNetCrossRefMATH

12.

I. Menshov and P. Zakharov, “On the composite Riemann problem for multimaterial fluid flows,” Int. J. N-umer. Methods Fluids 76 (2), 109–127 (2014). https://doi.org/10.1002/fld.3927CrossRefMATH

13.

B. A. Korneev, R. R. Tukhvatullina, and E. B. Savenkov, “Numerical study of two-phase hyperbolic models,” Math. Models Comput. Simul. 13 (6), 1002–1013 (2021). https://doi.org/10.1134/S2070048221060090MathSciNetCrossRef

14.

F. E. Marble, “Dynamics of dusty gases,” Annu. Rev. Fluid Mech. 2, 397–446 (1970). https://doi.org/10.1146/annurev.fl.02.010170.002145CrossRef

15.

G. M. Arutyunyan, “Conditions of applicability of the results of the hydrodynamics of a perfect gas to disperse media,” Fluid Dyn. 14 (1), 118–121 (1979). https://doi.org/10.1007/BF01050823CrossRef

16.

V. A. Vakhnenko and B. I. Palamarchuk, “Description of shock-wave processes in a two-phase medium containing an incompressible phase,” J. Appl. Mech. Tech. Phys. 25 (1), 101–107 (1984). https://doi.org/10.1007/BF00916876CrossRef

17.

A. S. Ivanov, V. V. Kozlov, and D. V. Sadin, “Unsteady flow of a two-phase disperse medium from a cylindrical channel of finite dimensions into the atmosphere,” Fluid Dyn. 31 (3), 386–391 (1996). https://doi.org/10.1007/BF02030221CrossRefMATH

18.

D. V. Sadin, Fundamentals of the Theory of Modeling Wave Heterogeneous Processes (Voen. Inzh.-Kosm. Univ., St. Petersburg, 2000) [in Russian].

19.

D. V. Sadin, “TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type,” Comput. Math. Math. Phys. 56 (12), 2068–2078 (2016). https://doi.org/10.1134/S0965542516120137MathSciNetCrossRefMATH

20.

D. V. Sadin, “Application of a hybrid large-particle method to the computation of the interaction of a shock wave with a gas suspension layer,” Komp. Issled. Model. 12 (6), 1323–1338 (2020). https://doi.org/10.20537/2076-7633-2020-12-6-1323-1338

21.

D. V. Sadin, “Efficient implementation of the hybrid large particle method,” Math. Models Comput. Simul. 14 (6), 946–954 (2022). https://doi.org/10.1134/S207004822206014XMathSciNetCrossRefMATH

22.

D. V. Sadin, “Stiffness problem in modeling wave flows of heterogeneous media with a three-temperature scheme of interphase heat and mass transfer,” J. Appl. Mech. Tech. Phys. 43 (2), 286–290 (2002). https://doi.org/10.1023/A:1014714012032CrossRefMATH

23.

D. V. Sadin, “A method for computing heterogeneous wave flows with intense phase interaction,” Comput. Math. Math. Phys. 38 (6), 987–993 (1998).MathSciNetMATH

24.

A. I. Ivandaev, A. G. Kutushev, and D. A. Rudakov, “Numerical investigation of throwing a powder layer by a compressed gas,” Combust. Explos. Shock Waves 31 (4), 459–465 (1995). https://doi.org/10.1007/BF00789367CrossRef

25.

D. V. Sadin, “On stiff systems of partial differential equations for motion of heterogeneous media,” Mat. Model. 14 (11), 43–53 (2002).MathSciNetMATH

Title: Test Problems of Gas Suspension Dynamics Using Asymptotically Exact Solutions
Author: D. V. Sadin
Publication date: 01-06-2023
Publisher: Pleiades Publishing
Published in: Mathematical Models and Computer Simulations / Issue 3/2023
Print ISSN: 2070-0482
Electronic ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048223030158

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