A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

doi:10.1007/s10483-024-3134-9

Abstract

Abstract:

Viscoelastic flows play an important role in numerous engineering fields, and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids. However, traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time, and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids. In this paper, a universal multiscale method coupling an improved smoothed particle hydrodynamics (SPH) and multiscale universal interface (MUI) library is presented for viscoelastic flows. The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain. We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows. In the first example, the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions. The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain. In the second example, the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics (DPD) method. The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain. Moreover, transferring different physical quantities has an important effect on the numerical results.

Key words: multiscale method, improved smoothed particle hydrodynamics (SPH), dissipative particle dynamics (DPD), multiscale universal interface (MUI), complex viscoelastic flow

2010 MSC Number:

Jinlian REN, Peirong LU, Tao JIANG, Jianfeng LIU, Weigang LU. A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1387-1402.

TrendMD

Figures/Tables 11

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

References 33

1	MORENO, N., and ELLERO, M. Generalized Lagrangian heterogenous multiscale modeling of complex fluids. Journal of Fluid Mechanics, 969, A2 (2023)
2	LEE, J., YOON, S., KWON, Y., and KIM, S. Practical comparison of differential viscoelastic constitutive equations in finite element analysis of planar 4: 1 contraction flow. Rheologica Acta, 44, 188- 197 (2004)
3	ZHUANG, X., OUYANG, J., LI, W., and LI, Y. Three-dimensional simulations of non-isothermal transient flow and flow-induced stresses during the viscoelastic fluid filling process. International Journal of Heat and Mass Transfer, 104, 374- 391 (2017)
4	FAVERO, J. L., SECCHI, A. R., CARDOZO, N. S. M., and JASAK, H. Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations. Journal of Non-Newtonian Fluid Mechanics, 165 (23-24), 1625- 1636 (2010)
5	ANAND, M., and RAJAGOPAL, K. R. A shear-thinning viscoelastic fluid model for describing the flow of blood. International Journal of Cardiovascular Medicine and Science, 4 (2), 59- 68 (2004)
6	JAVID, K., KOLSI, L., AI-KHALED, K., OMRI, M., KHAN, S., and ABBASI, A. Biomimetic propulsion of viscoelastic nanoparticles in a curved pump with curvature and slip effects: blood control bio-medical applications. Waves in Random and Complex Media, (2022) doi: 10.1080/17455030.2022.2028934
7	CLAUSEN, T. M., VINSON, P. K., MINTER, J. R., DAVIS, H. T., TALMON, Y., and MILLER, W. G. Viscoelastic micellar solutions: microscopy and rheology. The Journal of Physical Chemistry, 96 (1), 474- 484 (1992)
8	BALASUBRAMANIAN, S., KAUSHIK, P., and MONDAL, P. K. Dynamics of viscoelastic fluid in a rotating soft microchannel. Physics of Fluids, 32 (11), 112003 (2020)
9	AN, S., TIAN, K., DING, Z., and JIAN, Y. Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel. Applied Mathematics and Mechanics (English Edition), 43 (6), 917- 930 (2022) doi: 10.1007/s10483-022-2882-7
10	EENGQUIST, B., LI, X., REN, W., and VANDEN-EIJNDEN, E. Heterogeneous multiscale methods: a review. Communications in Computational Physics, 2 (3), 367- 450 (2007)
11	E, W. N, REN, W., and VANDEN-EIJDEN, E. A general strategy for designing seamless multiscale methods. Journal of Computational Physics, 228 (15), 5437- 5453 (2009)
12	BORG, M. K., LOCKERBY, D. A., and REESE, J. M. A hybrid molecular-continuum method for unsteady compressible multiscale flows. Journal of Fluid Mechanics, 768, 388- 414 (2015)
13	MORENO, N., VIGNAL, P., LI, J., and CALO, V. M. Multiscale modeling of blood flow: coupling finite elements with smoothed dissipative particle dynamics. Procedia Computer Science, 18, 2565- 2574 (2013)
14	LOCKERBY, D. A., DUQUE-DAZA, C. A., BORG, M. K., and REESE, J. M. Time-step coupling for hybrid simulations of multiscale flows. Journal of Computational Physics, 237, 344- 365 (2013)
15	BIAN, X., LITVINOV, S., QIAN, R., ELLERO, M., and ADAMS, N. A. Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics. Physics of Fluids, 24 (1), 012002 (2012)
16	INGELSTEN, S., MARK, A., KADAR, R., and EDELVIK, F. A backwards-tracking Lagrangian-Eulerian method for viscoelastic two-fluid flows. Applied Science, 11 (1), 439 (2021)
17	KULKARNI, P. M., FU, C. C., SHELL, M. S., and LEAL, L. G. Multiscale modeling with smoothed dissipative particle dynamics. The Journal of Chemical Physics, 138, 234105 (2013)
18	MULLER, K., FEDOSOV, D. A., and GOMPPER, G. Margination of micro- and nano-particles in blood flow and its effect on drug delivery. Scientific Reports, 4 (1), 4871 (2014)
19	MURASHIMA, T., and TANIGUCHI, T. Multiscale Lagrangian fluid dynamics simulation for polymeric fluid. Journal of Polymer Science, Part B: Polymer Physics, 48 (8), 886- 893 (2010)
20	MORII, Y., and KAWAKATSU, T. Lagrangian multiscale simulation of complex flows. Physics of Fluids, 33 (9), 093106 (2021)
21	XU, Y., ZHU, J., ZHENG, L., and SI, X. Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition. Applied Mathematics and Mechanics (English Edition), 41 (11), 1611- 1630 (2020) doi: 10.1007/s10483-020-2657-9
22	QIAO, Y., WANG, X., XU, H., and QI, H. Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models. Applied Mathematics and Mechanics (English Edition), 42 (12), 1771- 1786 (2021) doi: 10.1007/s10483-021-2796-8
23	REN, J., OUYANG, J., and JIANG, T. An improved particle method for simulation of the non-isothermal viscoelastic fluid mold filling process. International Journal of Heat and Mass Transfer, 85, 543- 560 (2015)
24	THOMAS, J. C., and ROWLEY, R. L. Transient molecular dynamics simulations of viscosity for simple fluids. The Journal of Chemical Physics, 127, 174510 (2007)
25	KHAN, M. B., SASMAL, C., and CHHABRA, R. P. Flow and heat transfer characteristics of a rotating cylinder in a FENE-P type viscoelastic fluid. Journal of Non-Newtonian Fluid Mechanics, 282, 104333 (2020)
26	FENG, H., ANDREEV, M., PILYUGINA, E., and SCHIEBER, J. D. Smoothed particle hydrodynamics simulation of viscoelastic flows with the slip-link model. Molecular Systems Design and Engineering, 1 (1), 99- 108 (2016)
27	TANG, Y. H., KUDO, S., BIAN, X., LI, Z., and KARNIADAKIS, G. E. Multiscale universal interface: a concurrent framework for coupling heterogeneous solvers. Journal of Computational Physics, 297, 13- 31 (2015)
28	LIU, G. R. and LIU, M. B. Smoothed Particle Hydrodynamics: a Mesh-free Particle Method, World Scientific, Singapore (2003)
29	JIANG, T., REN, J., YUAN, J., ZHOU, W., and WANG, D. S. A least-squares particle model with other techniques for 2D viscoelastic fluid/free surface flow. Journal of Computational Physics, 407, 109255 (2020)
30	HAYAT, T., KHAN, M., and AYUB, M. Exact solution of flow problems of an Oldroyd-B fluid. Applied Mathematics and Computation, 151 (1), 105- 119 (2004)
31	BIAN, X., LI, Z., and KARNIADAKIS, G. E. Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition. Journal of Computational Physics, 297, 132- 155 (2015)
32	SU, J., OUYANG, J., WANG, X., and YANG, B. Lattice Boltzmann method coupled with the Oldroyd-B constitutive model for a viscoelastic fluid. Physical Review E, 88 (5), 053304 (2013)
33	PARUSSINI, L., and PEDIRODA, V. Fictitious domain approach with hp-finite element approximation for incompressible fluid flow. Journal of Computational Physics, 228 (10), 3891- 3910 (2009)

[1]	Yuyi WANG, Jiangwei SHE, Zhewei ZHOU. A new model for dissipative particle dynamics boundary condition of walls with different wettabilities [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 467-484.
[2]	Yuda HU, Bingbing MA. Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 925-942.
[3]	M. ELLERO, P. ESPAÑOL. Everything you always wanted to know about SDPD^* (^*but were afraid to ask) [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(1): 103-124.
[4]	X. BIAN, Z. LI, N. A. ADAMS. A note on hydrodynamics from dissipative particle dynamics [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(1): 63-82.
[5]	D. AZARNYKH, S. LITVINOV, X. BIAN, N. A. ADAMS. Discussions on the correspondence of dissipative particle dynamics and Langevin dynamics at small scales [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(1): 31-46.
[6]	XIE Chun-Mei;FENG Min-Fu. New nonconforming finite element method for solving transient Naiver-Stokes equations [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 237-258.
[7]	DING Liang;HAN Bo;LIU Jia-Qi. A wavelet multiscale method for inversion of Maxwell equations [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(8): 1035-1044.