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

• Published in: Applied mathematics and mechanics Vol. 45; no. 8; pp. 1387 - 1402
• Main Authors: Ren, Jinlian, Lu, Peirong, Jiang, Tao, Liu, Jianfeng, Lu, Weigang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024; Springer Nature B.V
• Edition: English ed.
• Subjects: Algorithms; Applications of Mathematics; Classical Mechanics; Coupling; Exchanging; Fluid flow; Fluid mechanics; Fluid- and Aerodynamics; Laminar flow; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Multiscale analysis; Nonlinear dynamics; Partial Differential Equations; Relaxation time; Smooth particle hydrodynamics; Solvers; Viscoelastic fluids; Viscoelasticity; multiscale method; 76A10; O373; 76M28; multiscale universal interface (MUI); improved smoothed particle hydrodynamics (SPH); 35Q30; dissipative particle dynamics (DPD); complex viscoelastic flow
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-024-3134-9

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.