Grid structure optimization by the test particle method in the tasks of rarefied gas dynamics
Heading:
| 1Pecheritsa, LL, 1Smelaya, ТG 1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine |
| Space Sci. & Technol. 2020, 26 ;(1):48-58 |
| https://doi.org/10.15407/knit2020.01.048 |
| Publication Language: Russian |
Abstract: The inability to obtain the analytical solution of the integro-differential Boltzmann equation in general formulation stimulates both the continuous development and improvement of the traditionally used approaches and the search for new possibilities of the solution of this equation. In rarefied gas dynamics, the most widespread statistical method of the Boltzmann equation solution is the method of the direct Monte Carlo simulation. This article is devoted to the alternative statistical method of test-particle simulations (MTPS).
The paper aims to review previously obtained results of the Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine on MTPS development applying two-tier hierarchical adaptive grids. The article summarizes the main features of MTPS and gives the overview of works, which included the choice of the optimal computational grid for MTPS and its generation algorithm, the creation of new numeric algorithms for the tracking of molecule paths during the computational domain discretization using two-tier hierarchical adaptive grids, testing the MTPS algorithm with chosen grids at the 2D setting. Calculation results of the gas dynamic parameters in the vicinity of obstacles anddrag coefficients were compared with other results obtained both numerically and experimentally. The high quality of the tested computational algorithm is confirmed by the good accordance with the compared results. The use of the improved grids brings undeniable benefits in the application of MTPS, significantly reducing algorithm requirements to the resource. That allows you to cover a wider range of calculated flow regime and move on to solving new problems. The developed algorithms can be used in practical calculations of parameters of the environmental impact on spacecraft with complex shapes (including their parts) in the intervals of regimes from free molecular to near to transitional. |
| Keywords: adaptive hierarchical grids, Boltzmann equation, free molecular and transitional regimes, gas-dynamic parameters, the rarefied gas dynamics, the test particles method |
References:
1. Alexeeva E. V., Barantsev R. G. (1976). Local method of aerodynamic calculation in rarefied gas. Leningrad: LSU [in Russian].
2. Bass V. P., Pecheritsa L. L. (2010). Aerogasdynamic characteristics of “Sich-2” satellite while entering Earth’s atmosphere. Technical Mechanics, 3, 3—10 [in Russian].
3. Bass V. P., Pecheritsa L. L. (2010). Numerical solution of three-dimensional tasks of the rarefied gas dynamics. Technical Mechanics, 2, 38—51 [in Russian].
4. Bass V. P., Pecheritsa L. L., Smila T. G. (2012). Application of the unstructured grids for the simulation of the rarefied gas flows. The Models and Methods of the Aerodynamics: Proc. 12th International School-Seminar. Moscow, 2012. P. 22—23 [in
Russian].
5. Vlasov V. I. (1966). Improvement of statistical tests method (Monte-Carlo) for the calculation of the rarefied gases flows. Paper of the Academy of Sciences of USSR, 167(5), 1016—1018 [in Russian].
6. Vlasov V. I. (1986). Conservative variant of test particle method (Monte-Carlo). Numerical and Analytical Methods in the Rarefied Gas Dynamics: Proc. from 8th All-Union Conference on Rarefied Gas Dynamics (1986). Moscow, 81—85 [in Russian].
7. Hryhoriev Yu. N., Ivanov M. S., Haritonova N. M. (1971). The Numeral methods of continuum mechanics. Computing Center of the Siberian Branch of the USSR Academy of Sciences, 2(4), 101—107 [in Russian].
8. Gusev V. N., Yehorov I. V., Yerofeev A. I., Provotorov V. P. (1999). Verification of models and methods in the rarefied gas dynamics. Bulletin of the Russian Academy of Sciences. Fluid mechanics, 2, 129—134 [in Russian].
9. Yehorov I. V., Yerofeev A. I. (1997). Comparison of numerical simulation of hypersonic flow around the flat plate on the basis of the Monte-Carlo method and Navier-Stokes equations. Bulletin of the Russian Academy of Sciences. Fluid mechanics, 1, 133—145 [in Russian].
10. Kogan M. N. (1967). Rarefied gas dynamics. Kinetic theory. Moscow: Nauka [in Russian].
11. Koshmarov Yu. A., Ryzhov Yu. A. (1977). Applied dynamics of rarefied gas. Moscow: Mashinostroenie [in Russian].
12. Paliy O. S., Pecheritsa L. L. (2017). Application of the test particles method to the SV aerodynamics computation. Technical Mechanics, 3, 64—70 [in Russian].
2. Bass V. P., Pecheritsa L. L. (2010). Aerogasdynamic characteristics of “Sich-2” satellite while entering Earth’s atmosphere. Technical Mechanics, 3, 3—10 [in Russian].
3. Bass V. P., Pecheritsa L. L. (2010). Numerical solution of three-dimensional tasks of the rarefied gas dynamics. Technical Mechanics, 2, 38—51 [in Russian].
4. Bass V. P., Pecheritsa L. L., Smila T. G. (2012). Application of the unstructured grids for the simulation of the rarefied gas flows. The Models and Methods of the Aerodynamics: Proc. 12th International School-Seminar. Moscow, 2012. P. 22—23 [in
Russian].
5. Vlasov V. I. (1966). Improvement of statistical tests method (Monte-Carlo) for the calculation of the rarefied gases flows. Paper of the Academy of Sciences of USSR, 167(5), 1016—1018 [in Russian].
6. Vlasov V. I. (1986). Conservative variant of test particle method (Monte-Carlo). Numerical and Analytical Methods in the Rarefied Gas Dynamics: Proc. from 8th All-Union Conference on Rarefied Gas Dynamics (1986). Moscow, 81—85 [in Russian].
7. Hryhoriev Yu. N., Ivanov M. S., Haritonova N. M. (1971). The Numeral methods of continuum mechanics. Computing Center of the Siberian Branch of the USSR Academy of Sciences, 2(4), 101—107 [in Russian].
8. Gusev V. N., Yehorov I. V., Yerofeev A. I., Provotorov V. P. (1999). Verification of models and methods in the rarefied gas dynamics. Bulletin of the Russian Academy of Sciences. Fluid mechanics, 2, 129—134 [in Russian].
9. Yehorov I. V., Yerofeev A. I. (1997). Comparison of numerical simulation of hypersonic flow around the flat plate on the basis of the Monte-Carlo method and Navier-Stokes equations. Bulletin of the Russian Academy of Sciences. Fluid mechanics, 1, 133—145 [in Russian].
10. Kogan M. N. (1967). Rarefied gas dynamics. Kinetic theory. Moscow: Nauka [in Russian].
11. Koshmarov Yu. A., Ryzhov Yu. A. (1977). Applied dynamics of rarefied gas. Moscow: Mashinostroenie [in Russian].
12. Paliy O. S., Pecheritsa L. L. (2017). Application of the test particles method to the SV aerodynamics computation. Technical Mechanics, 3, 64—70 [in Russian].
13. Pecheritsa L. L. (2015). Simulation of the rarefied gas flows by the test particles method on the two-tier locally-structured grid. Abstracts of 15th Ukrainian conference on Space Research. (Kyiv, 2015). Kyiv. P. 114 [in Russian].
14. Pecheritsa L. L., Smila T. G. (2016). The numeral simulation of the axisymmetrical flow around extended compound body by test particles method with the use of hierarchical grids. Technical Mechanics, 2, 64—70 [in Russian].
15. Pecheritsa L. L., Smila T. G. (2016). The numeral simulation of the axisymmetrical flow around simply-shaped bodies with the use of hierarchical grids. Technical Mechanics, 1, 95—102 [in Russian].
16. Pecheritsa L. L., Smila T. G., Petrushenko N. V. (2013). Optimal algorithms construction of the test particles method realization in the rarefied gas dynamics. Modern Problems of the Rarefied Gas Dynamics: Proc. from the 4th All-Russian Conf. (Novosibirsk, 2013). Novosibirsk, 164—166 [in Russian].
17. Smila T. G. (2014). Adaptation of calculating grids to geometry of the streamlined obstacles. Abstracts of 15th Ukrainian conference on Space Research (Kyiv, 2014). Kyiv, 99 [in Russian].
18. Smila T. G. (2013). Choice of calculation grid at the simulation of the rarefied gas flows by the test particles method. Technical Mechanics, 1, 45—60 [in Russian].
19. Smila T. G. (2015). Unstructured grids and their application at the numeral simulation by the test particles method. Technical Mechanics, 4, 155—168 [in Russian].
20. Haviland J. K. (1969). Solution of two tasks on a molecular flow by the Monte-Carlo method. The computing methods in the rarefied gases dynamics. Moscow: Mir, 7—115 [in Russian].
21. Haviland J. K. (1962). Application of the Monte-Carlo method to heat transfer in a rarefied gas. Phys. Fluid, 5(11), 1399—1405.
14. Pecheritsa L. L., Smila T. G. (2016). The numeral simulation of the axisymmetrical flow around extended compound body by test particles method with the use of hierarchical grids. Technical Mechanics, 2, 64—70 [in Russian].
15. Pecheritsa L. L., Smila T. G. (2016). The numeral simulation of the axisymmetrical flow around simply-shaped bodies with the use of hierarchical grids. Technical Mechanics, 1, 95—102 [in Russian].
16. Pecheritsa L. L., Smila T. G., Petrushenko N. V. (2013). Optimal algorithms construction of the test particles method realization in the rarefied gas dynamics. Modern Problems of the Rarefied Gas Dynamics: Proc. from the 4th All-Russian Conf. (Novosibirsk, 2013). Novosibirsk, 164—166 [in Russian].
17. Smila T. G. (2014). Adaptation of calculating grids to geometry of the streamlined obstacles. Abstracts of 15th Ukrainian conference on Space Research (Kyiv, 2014). Kyiv, 99 [in Russian].
18. Smila T. G. (2013). Choice of calculation grid at the simulation of the rarefied gas flows by the test particles method. Technical Mechanics, 1, 45—60 [in Russian].
19. Smila T. G. (2015). Unstructured grids and their application at the numeral simulation by the test particles method. Technical Mechanics, 4, 155—168 [in Russian].
20. Haviland J. K. (1969). Solution of two tasks on a molecular flow by the Monte-Carlo method. The computing methods in the rarefied gases dynamics. Moscow: Mir, 7—115 [in Russian].
21. Haviland J. K. (1962). Application of the Monte-Carlo method to heat transfer in a rarefied gas. Phys. Fluid, 5(11), 1399—1405.