Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions

Journal of Computational Physics

Volumn 256, Issue , 2014, Pages 17-33

  Titarev, Vladimir ^a,b   Dumbser, Michael ^c   Utyuzhnikov, Sergey ^b,d  

^a DORODNICYN COMPUTING CENTER   (Russian Federation)

^b MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

^c UNIVERSITY OF TRENTO   (Italy)

^d UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Implicit; Kinetic; Micro; Parallel; Rarefied; Re entry vehicle; S model; Unstructured

Indexed keywords

BOLTZMANN EQUATION; FLOW OF GASES; INTEGRAL EQUATIONS; REENTRY; SUPERSONIC AIRCRAFT;

IMPLICIT; KINETIC SOLVERS; MICRO; PARALLEL; PARALLELIZATION STRATEGIES; RAREFIED; RAREFIED GAS FLOW; RE-ENTRY VEHICLES; S MODELS; UNSTRUCTURED;

KINETICS;

EID: 84884251158     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2013.08.051     Document Type: Article

References (50)

1. Aoki K., Kanba K., Takata S. Numerical analysis of a supersonic rarefied gas flow past a flat plate. Phys. Fluids 1997, 9(4):1144-1161.
2. Aristov V., Frolova A., Zabelok S., Arslanbekov R., Kolobov V. Simulations of pressure-driven flows through channels and pipes with unified flow solver. Vacuum 2012, 86(11):1717-1724. (special issue "Vacuum Gas Dynamics: Theory, Experiments and Practical Applications").
3. Aristov V., Zabelok S. A deterministic method for solving the Boltzmann equation with parallel computations. Comput. Math. Math. Phys. 2002, 42(3):406-418.
4. Barth T., Frederickson P. Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. 28th Aerospace Sciences Meeting 1990, AIAA paper No. 90-0013.
5. Bhatnagar P., Gross E., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 1954, 94(511):1144-1161.
6. Bosnyakov S., Kursakov I., Lysenkov A., Matyash S., Mikhailov S., Vlasenko V., Quest J. Computational tools for supporting the testing of civil aircraft configurations in wind tunnels. J. Prog. Aerosp. Sci. 2008, 44:67-120.
7. Clausing P. Über die stromung sehr verdunnter gase durch röhren von beliebiger länge. Ann. Phys. 1932, 32:961-989.
8. Dumbser M., Käser M., Titarev V., Toro E. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J. Comput. Phys. 2007, 226:204-243.
9. Filimon A., Dumbser M., Munz C. High-order finite volume schemes based on defect corrections. Z. Angew. Math. Mech. 2013, 93(6-7):423-436.
10. Fujimoto T., Usami M. Rarefied gas flow through a circular orifice and short tubes. J. Fluids Eng. 1984, 106(4):367-373.
11. Gusarov A., Smurov I. Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer. Phys. Fluids 2002, 14(12):4242-4255.
12. Karypis G., Kumar V. Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 1998, 48:96-129.
13. Kloss Y., Martynov D.V., Cheremisin F. Computer simulation and analysis of the Holweck pump in the transient regime. Tech. Phys. 2012, 82(4):451-456.
14. Kolgan V. Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics. Trans. Central Aerohydrodyn. Inst. 1972, 3(6):68-77. (in Russian).
15. Kolgan V. Finite-difference schemes for computation of three dimensional solutions of gas dynamics and calculation of a flow over a body under an angle of attack. Trans. Central Aerohydrodyn. Inst. 1975, 6(2):1-6. (in Russian).
16. Kolgan V. Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics. J. Comput. Phys. 2011, 230(7):2384-2390.
17. Kolobov V., Arslanbekov R., Aristov V., Frolova A., Zabelok S. Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement. J. Comput. Phys. 2007, 223:589-608.
18. Koshamarov Y., Ryzhov Y. Applied Rarefied Gas Dynamics 1977, Mashinostroenie, Moscow, (in Russian).
19. Larina I., Rykov V. Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom. Comput. Math. Math. Phys. 2010, 50(12):2118-2130.
20. Li Z.-H., Zhang H.-X. Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation. Int. J. Numer. Methods Fluids 2003, 42(4):361-382.
21. Men'shov I., Nakamura Y. An implicit advection upwind splitting scheme for hypersonic air flows in thermochemical nonequilibrium. A Collection of Technical Papers of 6th Int. Symp. on CFD, vol. 2 1995, 815.
22. Men'shov I., Nakamura Y. On implicit Godunov's method with exactly linearized numerical flux. Comput. Fluids 2000, 29(6):595-616.
23. Mieussens L. Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics. Math. Models Methods Appl. Sci. 2000, 8(10):1121-1149.
24. Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J. Comput. Phys. 2000, 162(2):429-466.
25. Pavlukhin P., Menshov I. Efficient parallel implementation of the LU-SGS method for gas dynamics problems. Sci. News MGTU GA 2011, 165:46-54. (in Russian).
26. Petrovskaya N., Wolkov A. The impact of grid geometry on the accuracy of higher order finite-volume and finite element schemes. Math. Model. 2010, 22(3):145-160. (in Russian).
27. Rodionov A. Complement to the Kolgan project. J. Comput. Phys. 2012, 231:4465-4468.
28. Rykov V. A model kinetic equation for a gas with rotational degrees of freedom. Fluid Dyn. 1975, 10(6):959-966.
29. Shakhov E. Approximate kinetic equations in rarefied gas theory. Fluid Dyn. 1968, 3(1):112-115.
30. Shakhov E. Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 1968, 3(5):95-96.
31. Shakhov E. Transverse flow of a rarefied gas around a plate. Fluid Dyn. 1972, 7(6):961-966.
32. Shakhov E. The axisymmetric non-linear steady flow of a rarefied gas in a pipe of circular cross section. Comput. Math. Math. Phys. 1996, 36(8):1123-1131.
33. Sharipov F. Benchmark problems in rarefied gas dynamics. Vacuum 2012, 86(11):1697-1700. (special issue "Vacuum Gas Dynamics: Theory, Experiments and Practical Applications").
34. Sharov D., Luo H., Baum J.D., Löhner R. Implementation of unstructured grid GMRES+LU-SGS method on shared-memory, cache-based parallel computers. 38th Aerospace Sciences Meeting and Exhibit January 2000, 10-13. (AIAA-2000-927).
35. Tillaeva N. A generalization of the modified Godunov scheme to arbitrary unstructured meshes. Trans. Central Aerohydrodyn. Inst. 1986, 17(2):18-26. (in Russian).
36. Titarev V. Towards fully conservative numerical methods for the nonlinear model Boltzmann equation 2003, 13. Preprint NI03031-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, UK.
37. Titarev V. Conservative numerical methods for model kinetic equations. Comput. Fluids 2007, 36(9):1446-1459.
38. Titarev V. Implicit numerical method for computing three-dimensional rarefied gas flows using unstructured meshes. Comput. Math. Math. Phys. 2010, 50(10):1719-1733.
39. Titarev V. Efficient deterministic modelling of three-dimensional rarefied gas flows. Commun. Comput. Phys. 2012, 12(1):161-192.
40. Titarev V. Implicit high-order method for calculating rarefied gas flow in a planar microchannel. J. Comput. Phys. 2012, 231(1):109-134.
41. Titarev V. Rarefied gas flow in a circular pipe of finite length. Vacuum 2013, 94:92-103.
42. Titarev V., Shakhov E. Computational study of a rarefied gas flow through a long circular pipe into vacuum. Vacuum 2012, 86(11):1709-1716. (special issue "Vacuum Gas Dynamics: Theory, Experiments and Practical Applications").
43. Vaganov A., Drozdov S., Kosykh A., Nersesov G.G., Chelysheva I., Yumashev V.L. Numerical simulation of aerodynamics of winged re-entry space vehicle. TsAGI Sci. J. 2009, 40(2):131-149.
44. Vaganov A., Drozdov S., Zadonsky S., Chelysheva I., Kosykh A., Nersesov G., Yumashev V. The study of aerodynamics of the aerospace vehicle with a deflected balancing flap. TsAGI Sci. J. 2009, 40(5):517-534.
45. van Leer B. Towards the ultimate conservative difference scheme V: a second order sequel to Godunov's method. J. Comput. Phys. 1979, 32:101-136.
46. van Leer B. A historical oversight: Vladimir P. Kolgan and his high-resolution scheme. J. Comput. Phys. 2011, 230(7):2378-2383.
47. Varoutis S., Valougeorgis D., Sazhin O., Sharipov F. Rarefied gas flow through short tubes into vacuum. J. Vac. Sci. Technol. 2008, 26(1):228-238.
48. Varoutis S., Valougeorgis D., Sharipov F. Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios. J. Vac. Sci. Technol. A 2009, 27(6):1377-1391.
49. Venkatakrishnan V. On the accuracy of limiters and convergence to steady-state solutions. 31st Aerospace Science Meeting & Exhibit 1993, AIAA paper 93-0880.
50. Vlasenko V. On mathematical basis and principles of construction of numerical methodologies in the applied package EWT-TsAGI. Tr. TsAGI 2007, 2671:20-85.