Transport diffuse interface model for simulation of solid-fluid interaction

doi:10.1007/s10483-019-2443-9

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (3): 321-330.doi: https://doi.org/10.1007/s10483-019-2443-9

Transport diffuse interface model for simulation of solid-fluid interaction

Li LI, Qian CHEN, Baolin TIAN

Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2018-09-14 修回日期:2018-10-30 出版日期:2019-03-01 发布日期:2019-03-01
通讯作者: Baolin TIAN E-mail:tian_baolin@iapcm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702029, 11771054, U1730118, 91852207, and 11801036) and the China Postdoctoral Science Foundation (No. 2016M600967)

Transport diffuse interface model for simulation of solid-fluid interaction

Li LI, Qian CHEN, Baolin TIAN

Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2018-09-14 Revised:2018-10-30 Online:2019-03-01 Published:2019-03-01
Contact: Baolin TIAN E-mail:tian_baolin@iapcm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702029, 11771054, U1730118, 91852207, and 11801036) and the China Postdoctoral Science Foundation (No. 2016M600967)

摘要/Abstract

摘要： For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0=0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves, such as shear waves in fluids, are introduced by the artificial treatment. In this paper, a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.

关键词: laminar flow, entrance region, velocity distribution, pressure loss, entrance length, solid-fluid interaction, phase-density equation, Eulerian method, diffuse interface model, neisen equation of state (EOS), MieGrü

Abstract: For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0=0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves, such as shear waves in fluids, are introduced by the artificial treatment. In this paper, a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.

Key words: laminar flow, entrance region, velocity distribution, pressure loss, entrance length, phase-density equation, Eulerian method, diffuse interface model, solid-fluid interaction, MieGrüneisen equation of state (EOS)

中图分类号:

74F10

Li LI, Qian CHEN, Baolin TIAN. Transport diffuse interface model for simulation of solid-fluid interaction[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(3): 321-330.

参考文献

[1] LEE, C. B. and WU, J. Z. Transition in wall-bounded flows. Advances in Mechanics, 61(3), 683-695(2009)
[2] BATRA, R. C. and STEVENS, J. B. Adiabatic shear bands in axisymmetric impact and penetration problems. Computer Methods in Applied Mechanics & Engineering, 151(3-4), 325-342(1998)
[3] SCHOCH, S., NIKIFORAKIS, N., and LEE, B. J. The propagation of detonation waves in nonideal condensed-phase explosives confined by high sound-speed materials. Physics of Fluids, 25(8), 452-457(2013)
[4] DIMONTE, G., TERRONES, G., CHERNE, F. J., GERMANN, T. C., DUPONT, V., KADAU, K., BUTTLER, W. T., ORO, D. M., MORRIS, C., and PRESTON, D. L. Use of the RichtmyerMeshkov instability to infer yield stress at high-energy densities. Physical Review Letters, 107(26), 264502(2011)
[5] LEE, C. B., PENG, H. W., YUAN, H. J., WU, J. Z., ZHOU, M. D., and FAZLE, H. Experimental studies of surface waves inside a cylindrical container. Journal of Fluid Mechanics, 677(3), 39-62(2011)
[6] LEE, C. B., SU, Z., ZHONG, H. J., CHEN, S. Y., ZHOU, M. D., and WU, J. Z. Experimental investigation of freely falling thin disks, part 2:transition of three-dimensional motion from zigzag to spiral. Journal of Fluid Mechanics, 732(5), 77-104(2013)
[7] GHAISAS, N. S., SUBRAMANIAM, A., and LELE, S. K. A unified high-order Eulerian method for continuum simulations of fluid flow and of elastic-plastic deformations in solids. Journal of Computational Physics, 371(22), 452-482(2018)
[8] LI, X. L., FU, D. X., and MA, Y. W. Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack. Physics of Fluids, 22(2), 025105(2010)
[9] BARLOW, A. J., MAIRE, P. H., RIDER, W. J., RIEBEN, R. N., and SHASHKOV, M. J. Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows. Journal of Computational Physics, 322, 603-665(2016)
[10] GHAISAS, N. S., SUBRAMANIAM, A., and LELE, S. K. High-order Eulerian methods for elasticplastic flow in solids and coupling with fluid flows. 46th AIAA Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, Washington, D. C. (2016)
[11] GODUNOV, S. K. and ROMENSKⅡ, E. I. Elements of Continuum Mechanics and Conservation Laws, Kluwer Academic/Plenum Publishers, New York (2003)
[12] PLOHR, B. J. and SHARP, D. H. A conservative Eulerian formulation of the equations for elastic flow. Advances in Applied Mathematics, 9(4), 481-499(1988)
[13] HIRT, C. W. and NICHOLS, B. D. Volume of fluid method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201-225(1981)
[14] BARTON, P. T., DEITERDING, R., MEIRON, D., and PULLIN, D. Eulerian adaptive finitedifference method for high-velocity impact and penetration problems. Journal of Computational Physics, 240(5), 76-99(2013)
[15] ABGRALL, R. How to prevent pressure oscillations in multicomponent flow calculations:a quasi conservative approach. Journal of Computational Physics, 125(1), 150-160(1994)
[16] BAER, M. R. and NUNZIATO, J. W. A two-phase mixture theory for the deflagration-todetonation transition (DDT) in reactive granular materials. International Journal of Multiphase Flow, 12(6), 861-889(1986)
[17] SAUREL, R. and ABGRALL, R. A multiphase Godunov method for compressible multifluid and multiphase flows. Journal of Computational Physics, 150(2), 425-467(1999)
[18] SAUREL, R., PETITPAS, F., and BERRY, R. A. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. Journal of Computational Physics, 228(5), 1678-1712(2009)
[19] KAPILA, A. K., MENIKOFF, R., BDZIL, J. B., SON, S. F., and STEWART, D. S. Two-phase modeling of deflagration-to-detonation transition in granular materials:reduced equations. Physics of Fluids, 13(10), 3002-3024(2001)
[20] MURRONE, A. A five equation reduced model for compressible two phase flow problems. Journal of Computational Physics, 202(2), 664-698(2005)
[21] FAVRIE, N., GAVRILYUK, S. L., and SAUREL, R. Solid-fluid diffuse interface model in cases of extreme deformations. Journal of Computational Physics, 228(16), 6037-6077(2009)
[22] FAVRIE, N. and GAVRILYUK, S. L. Diffuse interface model for compressible fluid-compressible elastic-plastic solid interaction. Journal of Computational Physics, 231(7), 2695-2723(2012)
[23] NDANOU, S., FAVRIE, N., and GAVRILYUK, S. Multi-solid and multi-fluid diffuse interface model:applications to dynamic fracture and fragmentation. Journal of Computational Physics, 295(25), 523-555(2015)
[24] KLUTH, G. and DESPRÉS, B. Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme. Journal of Computational Physics, 229(1), 9092-9118(2010)
[25] ABGRALL, R. and KARNI, S. Computations of compressible multifluids. Journal of Computational Physics, 169(2), 594-623(2001)
[26] SHYUE, K. M. An efficient shock-capturing algorithm for compressible multicomponent problems. Journal of Computational Physics, 142(1), 208-242(1998)
[27] SHYUE, K. M. Regular article:a fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state. Journal of Computational Physics, 156(1), 43-88(1999)
[28] SHYUE, K. M. A fluid-mixture type algorithm for compressible multicomponent flow with MieGrüneisen equation of state. Journal of Computational Physics, 171(2), 678-707(2001)
[29] MAIRE, P. H. and REBOURCET, B. A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids. Journal of Computational Physics, 235(2), 626-665(2013)
[30] HE, Z. W., ZHANG, Y. S., LI, X. L., LI, L., and TIAN, B. L. Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities. Journal of Computational Physics, 300(5), 269-287(2015)

Transport diffuse interface model for simulation of solid-fluid interaction

Transport diffuse interface model for simulation of solid-fluid interaction

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Hongxia GUO, Ping LIN, Lin LI. Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1147-1164.
[2]	Xinyin ZOU, Xiang QIU, Jianping LUO, Jiahua LI, P. N. KALONI, Yulu LIU. Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 169-180.
[3]	Wei-jie WANG;Wen-xin HUAI;Yu-hong ZENG;Ji-fu ZHOU. Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 107-120.
[4]	C. STELIAN;于洋;李本文;A. THESS. Influence of velocity profile on calibration function ofLorentz force flowmeter [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 993-1004.
[5]	赵轲高正红黄江涛. Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 191-202.
[6]	H. NEMATI;M. FARHADI;K. SEDIGHI;M. M. PIROUZ;N. N. ABATARI. Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 427-444.
[7]	R. ANSARI;E. KAZEMI. Detailed investigation on single water molecule entering carbon nanotubes[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1287-1300.
[8]	槐文信耿川曾玉红杨中华. Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(4): 459-468.
[9]	M.GORJI M.ALIPANAH M.SHATERI E.FARNAD. Analytical solution for laminar flow through leaky tube[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(1): 69-74.
[10]	杨中华高伟槐文信. Secondary flow coefficient of overbank flow[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(6): 709-718.
[11]	万五一朱嵩胡云进. Attenuation analysis of hydraulic transients with laminar-turbulent flow alternations[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(10): 1209-1216.
[12]	槐文信;韩杰;曾玉红;安翔;钱忠东. Velocity distribution of flow with submerged flexible vegetations based on mixing-length approach[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(3): 343-351.
[13]	孟庆国. ANALYTIC SOLUTIONS OF INCOMPRESSIBLE LAMINAR FLOW IN THE INLET REGION OF A PIPE[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(8): 894-897.
[14]	邓松圣;周绍骑;廖振方;邱正阳;曾顺鹏. THEORETICAL ANALYSIS ON HYDRAULIC TRANSIENT RESULTED BY SUDDEN INCREASE OF INLET PRESSURE FOR LAMINAR PIPELINE FLOW[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 672-678.
[15]	白玉川;罗纪生. THE LOSS OF STABILITY OF LAMINAR FLOW IN OPEN CHANNEL AND THE MECHANISM OF SAND RIPPLE FORMATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(3): 276-293.