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Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form. (English) Zbl 1440.76098
Summary: The topic of the paper is accuracy analysis of acoustic propagation simulation in low Mach number flows, by finite volume co-located discretisation methods of the time-dependent compressible fluid Euler equations that use the concept of convection-pressure splitting (CPS). These are algorithms that split the flux vectors into a part associated to the convection by the fluid particles, and a part associated to the propagation of the pressure waves. For the convection part, the appropriate space discretisation is the upwind one. For the pressure part, there are alternatives. We discern five types of algorithms that all are adapted for use in low Mach number flows, and thus are considered as all Mach number algorithms. We study the behaviour of the different types for the propagation of small pressure perturbations, of discontinuous or smooth shape, in low Mach number flows. We demonstrate that four of the proposed algorithms of convection-pressure split type are dissipative for such applications, although they are designed for low Mach number flows. The objective of the paper is to analyse why some algorithms are appropriate for acoustic propagation simulation and why some are not appropriate.
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
76N15 Gas dynamics, general
Full Text: DOI
[1] Wesseling, P., Principles of Computational Fluid Dynamics (2001), Springer
[2] Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics (2009), Springer · Zbl 1227.76006
[3] Guillard, H.; Viozat, C., On the behaviour of upwind schemes in the low Mach number limit, Comput. Fluids, 28, 63-86 (1999) · Zbl 0963.76062
[4] Guillard, H.; Murrone, A., On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes, Comput. Fluids, 33, 655-675 (2004) · Zbl 1049.76040
[5] Guillard, H.; Nkonga, B., On the behaviour of upwind schemes in the low Mach number limit: a review, (Abgrall, R.; Shu, C.-W., Handbook of Numerical Methods for Hyperbolic Problems. Handbook of Numerical Methods for Hyperbolic Problems, Handbook of Numerical Analysis, vol. 18 (2017), Elsevier), 203-231 · Zbl 1366.76061
[6] Steger, J. L.; Warming, R. F., Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J. Comput. Phys., 40, 263-293 (1981) · Zbl 0468.76066
[7] Zha, G.-C.; Bilgen, E., Numerical solution of Euler equations by using a new flux vector splitting scheme, Int. J. Numer. Methods Fluids, 17, 115-155 (1993) · Zbl 0779.76067
[8] Liou, M.-S.; Steffen, C. J., A new flux splitting scheme, J. Comput. Phys., 107, 23-39 (1993) · Zbl 0779.76056
[9] Toro, E. F.; Vázquez-Cendón, M. E., Flux splitting schemes for the Euler equations, Comput. Fluids, 70, 1-12 (2012) · Zbl 1365.76243
[10] Moguen, Y.; Kousksou, T.; Bruel, P.; Vierendeels, J.; Dick, E., Pressure-velocity coupling allowing acoustic calculation in low Mach number flow, J. Comput. Phys., 231, 5522-5541 (2012) · Zbl 1426.76406
[11] Moguen, Y.; Bruel, P.; Dick, E., A combined momentum-interpolation and advection upstream splitting pressure-correction algorithm for simulation of convective and acoustic transport at all levels of Mach number, J. Comput. Phys., 384, 16-41 (2019)
[12] Toro, E. F., The HLLC Riemann solver, Shock Waves, 29, 1065-1082 (2019)
[13] Kitamura, K.; Shima, E., AUSM-like expression of HLLC and its all-speed extension, Int. J. Numer. Methods Fluids, 92, 246-265 (2020)
[14] Chen, S.-s; Cai, F.-j.; Xue, H.-c.; Wang, N.; Yan, C., An improved AUSM-family scheme with robustness and accuracy for all Mach number flows, Appl. Math. Model., 77, 1065-1081 (2020) · Zbl 07193015
[15] Li, X.-s.; Gu, C.-w., Mechanism of Roe-type schemes for all-speed flows and its application, Comput. Fluids, 86, 56-70 (2013) · Zbl 1290.76102
[16] Shima, E.; Kitamura, K., New approaches for computation of low Mach number flows, Comput. Fluids, 85, 143-152 (2013) · Zbl 1290.76090
[17] Liou, M.-S., A sequel to AUSM: AUSM^+, J. Comput. Phys., 129, 364-382 (1996) · Zbl 0870.76049
[18] Liou, M.-S., A sequel to AUSM, part II: AUSM+ -up for all speeds, J. Comput. Phys., 214, 137-170 (2006) · Zbl 1137.76344
[19] Shima, E.; Kitamura, K., Parameter-free simple low-dissipation AUSM-family scheme for all speeds, AIAA J., 49, 1693-1709 (2011)
[20] Kitamura, K.; Shima, E., Towards shock-stable and accurate hypersonic heating computations: a new pressure flux for AUSM-family schemes, J. Comput. Phys., 245, 62-83 (2013) · Zbl 1349.76487
[21] Mandal, J. C.; Panwar, V., Robust HLL-type Riemann solver capable of resolving contact discontinuity, Comput. Fluids, 63, 148-164 (2012) · Zbl 1365.76164
[22] Sun, D.; Yan, C.; Qu, F.; Du, R., A robust flux splitting method with low dissipation for all-speed flows, Int. J. Numer. Methods Fluids, 84, 3-18 (2017)
[23] Ong, K. C.; Chan, A., A pressure-based Mach-uniform method for viscous fluid flows, Int. J. Comput. Fluid Dyn., 30, 516-530 (2016)
[24] Xiao, C.-N.; Denner, F.; van Wachem, B. G.M., Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries, J. Comput. Phys., 346, 91-130 (2017) · Zbl 1378.76061
[25] Denner, F.; Xiao, C. N.; van Wachem, B. G.M., Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation, J. Comput. Phys., 367, 192-234 (2018) · Zbl 1415.76466
[26] Bartholomew, P.; Denner, F.; Abdol-Azis, M. H.; Marquis, A.; van Wachem, B. G.M., Unified formulation of the momentum-weighted interpolation for collocated variable arrangements, J. Comput. Phys., 375, 177-208 (2018) · Zbl 1416.76137
[27] Li, X.-s.; Gu, C.-w., The momentum interpolation method based on the time-marching algorithm for all-speed flows, J. Comput. Phys., 229, 7806-7818 (2010) · Zbl 1425.76187
[28] Fleischmann, N.; Adami, S.; Hu, X. Y.; Adams, N. A., A low dissipation method to cure the grid-aligned shock, J. Comput. Phys., 401, Article 109004 pp. (2020)
[29] Li, X.-s.; Gu, C.-w., An all-speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour, J. Comput. Phys., 227, 5144-5159 (2008) · Zbl 1388.76207
[30] Rieper, F., A low-Mach number fix for Roe’s approximate Riemann solver, J. Comput. Phys., 230, 5263-5287 (2011) · Zbl 1419.76461
[31] Ren, X.-d.; Gu, C.-w.; Li, X.-s., Role of the momentum interpolation mechanism of the Roe scheme in shock instability, Int. J. Numer. Methods Fluids, 84, 335-351 (2017)
[32] Li, X.-s.; Ren, X.-d.; Gu, C.-w.; Li, Y.-h., Shock-stable Roe scheme combining entropy fix and rotated Riemann solver, AIAA J., 58, 779-786 (2020)
[33] Li, X.-s.; Ren, X.-d.; Gu, C.-w., Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism, Appl. Math. Mech., 39, 455-466 (2018) · Zbl 1391.76294
[34] Shen, Z.; Yan, W.; Yuan, G., A robust HLLC-type Riemann solver for strong shock, J. Comput. Phys., 309, 185-206 (2016) · Zbl 1351.76043
[35] Chen, S.-s; Yan, C.; Lin, B.-x.; Liu, L.-y.; Yu, J., Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenon, J. Comput. Phys., 373, 662-672 (2018) · Zbl 1416.76142
[36] Simon, S.; Mandal, J. C., A simple cure for numerical shock instability in the HLLC Riemann solver, J. Comput. Phys., 378, 477-496 (2019) · Zbl 1416.76160
[37] Xie, W.; Li, H.; Tian, Z.; Pan, S., A low diffusion flux splitting method for inviscid compressible flows, Comput. Fluids, 112, 83-93 (2015) · Zbl 1390.76534
[38] Xie, W.; Li, W.; Li, H.; Tian, Z.; Pan, S., On numerical instabilities of Godunov-type schemes for strong shocks, J. Comput. Phys., 350, 607-637 (2017) · Zbl 1380.76073
[39] Tam, C. K.W.; Webb, J. C., Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107, 262-281 (1993) · Zbl 0790.76057
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