Article
| Title: | An entropy stable finite volume method for a compressible two phase model (English) |
| Author: | Feireisl, Eduard |
| Author: | Petcu, Mădălina |
| Author: | She, Bangwei |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 467-483 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory. (English) |
| Keyword: | compressible Navier-Stokes-Allen-Cahn |
| Keyword: | finite volume method |
| Keyword: | entropy stability |
| MSC: | 65M12 |
| MSC: | 76N06 |
| MSC: | 76Txx |
| idZBL: | Zbl 07729507 |
| idMR: | MR4612743 |
| DOI: | 10.21136/AM.2023.0041-22 |
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| Date available: | 2023-07-10T14:12:34Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151705 |
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| Reference: | [1] Abels, H., Feireisl, E.: On a diffuse interface model for a two-phase flow of compressible viscous fluids.Indiana Univ. Math. J. 57 (2008), 659-698. Zbl 1144.35041, MR 2414331, 10.1512/iumj.2008.57.3391 |
| Reference: | [2] Blesgen, T.: A generalization of the Navier-Stokes equations to two-phase flow.J. Phys. D, Appl. Phys. 32 (1999), 1119-1123. 10.1088/0022-3727/32/10/307 |
| Reference: | [3] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.Classics in Applied Mathematics 40. SIAM, Philadelphia (2002). Zbl 0999.65129, MR 1930132, 10.1137/1.9780898719208 |
| Reference: | [4] Lukáčová-Medviďová, E. Feireisl M., Mizerová, H., She, B.: Convergence of a finite volume scheme for the compressible Navier-Stokes system.ESAIM, Math. Model. Numer. Anal. 53 (2019), 1957-1979 DOI 10.1051/m2an/2019043 Experiment 2: time evolution of $\vartheta_h$, from top to bottom are $t=0, 0.001, 0.1,1$. Zbl 1447.35243, MR 4031688, 10.1051/m2an/2019043 |
| Reference: | [5] Feireisl, E., Lukáčová-Medviďová, M., Mizerová, H., She, B.: Numerical Analysis of Compressible Fluid Flows.MS&A. Modeling, Simulation and Applications 20. Springer, Cham (2021). Zbl 1493.76001, MR 4390192, 10.1007/978-3-030-73788-7 |
| Reference: | [6] Feireisl, E., Lukáčová-Medviďová, M., Mizerová, H., She, B.: On the convergence of a finite volume method for the Navier-Stokes-Fourier system.IMA J. Numer. Anal. 41 (2021), 2388-2422. Zbl 07528308, MR 4328388, 10.1093/imanum/draa060 |
| Reference: | [7] Feireisl, E., Petcu, M., Pražák, D.: Relative energy approach to a diffuse interface model of a compressible two-phase flow.Math. Methods Appl. Sci. 42 (2019), 1465-1479. Zbl 1420.35185, MR 3928163, 10.1002/mma.5436 |
| Reference: | [8] Feireisl, E., Petcu, M., She, B.: Numerical analysis of a model of two phase compressible fluid flow.J. Sci. Comput. 89 (2021), Article ID 14, 32 pages. Zbl 1489.35183, MR 4304552, 10.1007/s10915-021-01624-7 |
| Reference: | [9] Feireisl, E., Petzeltová, H., Rocca, E., Schimperna, G.: Analysis of a phase-field model for two-phase compressible fluids.Math. Models Methods Appl. Sci. 20 (2010), 1129-1160. Zbl 1200.76155, MR 2673413, 10.1142/S0218202510004544 |
| Reference: | [10] VanderZee, E., Hirani, A. N., Guoy, D., Ramos, E. A.: Well-centered triangulation.SIAM J. Sci. Comput. 31 (2010), 4497-4523. Zbl 1253.65030, MR 2594991, 10.1137/090748214 |
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