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Mathematical Models and Computer Simulations

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01.12.2022

Efficient Implementation of the Hybrid Large Particle Method

verfasst von: D. V. Sadin

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 6/2022

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Abstract

Within the framework of the hybrid method of large particles, an efficient algorithm with controlled numerical dissipation of the second order of accuracy in space and time is proposed. The computational properties of the algorithm are tested on one-dimensional Einfeldt, Tang and Liu, LeBlanc, Shu and Osher test problems, as well as two-dimensional Riemann problems. The algorithm is robust and has a high resolution, comparable to modern schemes, which formally have a higher order of approximation.

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S. K. Godunov, “A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics,” Sb. Math. 47 (8–9), 357–393 (1959).

E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (Springer, Berlin, 2009). https://doi.org/10.1007/b79761CrossRefMATH

A. Harten, “High resolution schemes for hyperbolic conservation laws,” J. Comput. Phys. 49 (3), 357–393 (1983). https://doi.org/10.1016/0021-9991(83)90136-5MathSciNetCrossRefMATH

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

X.-D. Liu, S. Osher, and T. Chan, “Weighted essentially non-oscillatory schemes,” J. Comput. Phys. 115 (1), 200–212 (1994). https://doi.org/10.1006/jcph.1994.1187MathSciNetCrossRefMATH

J. Shi, Y.-T. Zhang, and C.-W. Shu, “Resolution of high order WENO schemes for complicated flow structures,” J. Comput. Phys. 186 (2), 690–696 (2003). https://doi.org/10.1016/S0021-9991(03)00094-9MathSciNetCrossRefMATH

B. Cockburn and C.-W. Shu, “Runge–Kutta discontinuous Galerkin methods for convection-dominated problems,” J. Sci. Comput. 16 (3), 173–261 (2001). https://doi.org/10.1023/A:1012873910884MathSciNetCrossRefMATH

M. E. Ladonkina, O. A. Neklyudova, and V. F. Tishkin, “Application of the RKDG method for gas dynamics problems,” Math. Models Comput. Simul. 6 (4), 397–407 (2014). https://doi.org/10.1134/S207004821404005XMathSciNetCrossRefMATH

R. P. Fedorenko, “The application of difference schemes of high accuracy to the numerical solution of hyperbolic equations,” USSR Comput. Math. Math. Phys. 2 (6), 1355–1365 (1963). https://doi.org/10.1016/0041-5553(63)90351-3CrossRefMATH

10.

X. Liu, S. Zhang, H. Zhang, and C.-W. Shu, “A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes,” J. Comput. Phys. 284, 133–154 (2015). https://doi.org/10.1016/j.jcp.2014.12.027MathSciNetCrossRefMATH

11.

Y. A. Kriksin and V. F. Tishkin, “Hybrid approach to solve single-dimensional gas dynamics equations,” Math. Models Comput. Simul. 11 (2), 256–265 (2019). https://doi.org/10.1134/S2070048219020078MathSciNetCrossRef

12.

B. N. Chetverushkin, “Hyperbolic quasi-gasdynamic system,” Math. Models Comput. Simul. 10 (5), 588–600 (2018). https://doi.org/10.1134/S2070048218050046MathSciNetCrossRef

13.

R. Liska and B. Wendroff, “Comparison of several difference schemes on 1D and 2D test problems for the Euler equations,” SIAM J. Sci. Comput. 25 (3), 995–1017 (2003). https://doi.org/10.1137/S1064827502402120MathSciNetCrossRefMATH

14.

H. Tang and T. Liu, “A note on the conservative schemes for the Euler equations,” J. Comput. Phys. 218 (2), 451–459 (2006). https://doi.org/10.1016/j.jcp.2006.03.035CrossRefMATH

15.

A. V. Danilin and A.V. Solov’ev, “A modification of the CABARET scheme for resolving the sound points in gas flows,” Vychisl. Metody Program. 20 (4), 481–488 (2019). https://doi.org/10.26089/NumMet.v20r442

16.

I. Yu. Tagirova and A. V. Rodionov, “Application of artificial viscosity for suppressing the carbuncle phenomenon in Godunov-type schemes,” Math. Models Comput. Simul. 8 (3), 249–262 (2016). https://doi.org/10.1134/S2070048216030091MathSciNetCrossRefMATH

17.

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

18.

D. V. Sadin, “Schemes with customizable dissipative properties as applied to gas-suspensions flow simulation,” Mat. Model. 29 (12), 89–104 (2017).MathSciNet

19.

D. V. Sadin, “Application of scheme with customizable dissipative properties for gas flow calculation with interface instability evolution,” Nauchno-Tekh. Vestn. Inf. Tekhnol., Mekh. Opt. 8 (1), 153–157 (2018). https://doi.org/10.17586/2226-1494-2018-18-1-153-157CrossRef

20.

D. V. Sadin, “A modification of the large-particle method to a scheme having the second order of accuracy in space and time for shockwave flows in a gas suspension,” Vestn. Yuzhno-Ural. Gos. Univ. Ser. Mat. Model. Program. 12 (2), 112–122 (2019). https://doi.org/10.14529/mmp190209CrossRefMATH

21.

D. V. Sadin and V. A. Davidchuk, “Comparison of a modified large-particle method with some high resolution schemes. One-dimensional test problems,” Vychisl. Metody Program. 20 (2), 138–146 (2019). https://doi.org/10.26089/NumMet.v20r214

22.

D. V. Sadin, I. O. Golikov, and E. N. Shirokova, “Testing of the hybrid large-particle method using two-dimensional Riemann problems,” St. Petersburg Polytech. State Univ. J. Phys. Math. 14 (1), 55–68 (2021). https://doi.org/10.18721/JPM.14104CrossRef

23.

D. V. Sadin, “Analysis of dissipative properties of a hybrid large-particle method for structurally complicated gas flows,” Komp. Issled. Model. 12 (4), 757–772 (2020). https://doi.org/10.20537/2076-7633-2020-12-4-757-772

24.

M. E. Ladonkina, O. A. Neklyudova, and V. F. Tishkin, “Constructing a limiter based on averaging the solutions for the discontinuous Galerkin method,” Math Models Comput. Simul. 11 (1), 61–73 (2019). https://doi.org/10.1134/S2070048219010101MathSciNetCrossRef

25.

S. A. Karabasov, “On the power of second-order accurate numerical methods for model problems of gas- and hydrodynamics,” Math. Models Comput. Simul. 3 (1), 92–112 (2011). https://doi.org/10.1134/S2070048211010078CrossRef

26.

Z. He, Y. Zhang, F. Gao, X. Li, and B. Tian, “An improved accurate monotonicity-preserving scheme for the Euler equations,” Comput. Fluids 140, 1–10 (2016). https://doi.org/10.1016/j.compfluid.2016.09.002MathSciNetCrossRefMATH

27.

J. A. Greenough and W. J. Rider, “A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov,” J. Comput. Phys. 196 (1), 259–281 (2004). https://doi.org/10.1016/j.jcp.2003.11.002MathSciNetCrossRefMATH

28.

X. Deng, B. Xie, R. Loubère, Y. Shimizu, and F. Xiao, “Limiter-free discontinuity-capturing scheme for compressible gas dynamics with reactive fronts,” Comput. Fluids 171, 1–14 (2018). https://doi.org/10.1016/j.compfluid.2018.05.015MathSciNetCrossRefMATH

Titel: Efficient Implementation of the Hybrid Large Particle Method
verfasst von: D. V. Sadin
Publikationsdatum: 01.12.2022
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 6/2022
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S207004822206014X

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