The 2021 Nobel Prize in physics, having been awarded to Syukuro Manabe and Klaus Hasselmann for their works on physical modeling of global climate and Giorgio Parisi for his work on complex physical systems, in some sense, emphasizes the significance of using numerical simulations to broaden our understanding of complex physical systems.

Prof. Sergio Galindo-Torres, who is currently the PI for the Multiscale Multiphysics Modeling Laboratory (M3Lab) in the School of Engineering, Westlake University, is working intensively to develop multiple numerical tools from grain-scale to continuum scale. He and his colleagues try to apply such a multiscale Multiphysics modeling system to different physical processes and help establish predicting models and problem solutions for complex systems in civil engineering, environmental engineering, mining engineering, and natural hazard mitigations.

Prof. Galindo-Torres and his group recently published one paper focusing on continuous modeling of fluid-solid interactions which can be applied to systems with high Reynolds number and large deformations and another paper improving our understanding of granular materials using grain-scale physical modeling. These two papers were published in Computer Methods in Applied Mechanics and Engineering, a top journal in computational mechanics, and Geophysical Research Letters, a top journal in earth science, respectively.

Fluid-solid coupled modeling with high Reynolds number and large deformations

Fluid-solid interaction (FSI) is ubiquitous in natural and engineering systems. Eagles rely on the interaction between the air and the wing to give them the lifting power. Sailfishes utilize the interaction between their fins and seawater to get the fastest swimming speed. Machines, such as planes and cruisers, all rely on our thorough understanding of solid mechanics, fluid mechanics, and the coupling of fluid and solid. Further, in the microscopic world, the modeling of blood transport, cell deformation, and the growth of tumors cannot be achieved without the development and utilization of fluid-solid coupling techniques.

However, most current FSI methods have difficulties in being applied to systems with high Reynold numbers, large deformations, and complex solid geometries. Dr. Pei Zhang, who is currently an associate research professor in Prof. Galindo-Torres’ group, developed a coupled method, which can combine the advantages of both the lattice-Boltzmann method (LBM) for modeling fluids and the material point method (MPM) for simulation solids. This coupling method has the following advantages:

(1) Lattice-Boltzmann method, a mesoscale method for simulating fluid mechanics, has advantages in dealing with complex geometries and moving boundaries. Besides, the solution of advection in LBM is exact which reduces the numerical diffusion errors in conventional computational fluid dynamics methods. the locality of the collision operator guarantees a high parallelization efficiency of LBM codes.

(2) Material point method, which is a particle-based method, can efficiently solve the mesh distortion problem due to large deformation, and meanwhile avoid complex neighbor search algorithms in traditional particle methods. Also, the setting of boundary conditions in MPM is similar to the finite element method, which is more direct and simpler than meshfree methods.

(3) This coupling scheme ensures the existence of a sharp interface between solids and liquids, which can help obtain accurate dynamical fluid-solid interactions on the interface and is helping to solve the problems due to the complex geometry.

In addition to the coupling scheme, this paper also provides interesting validation cases, from fixed-end beam simulations for validating the material point method to drag force calculate cases, which are common when validating fluid mechanics models in the lattice-Boltzmann method. The paper also shows simulations of the dynamics of soft bars vibrating in fluid with different Reynolds numbers (Fig. 1).

Different Reynold number in the fluid often leads to different vibration mode of the soft bar. The coupling scheme reported in the paper could capture accurate interaction between the fast-flowing fluid and the large-deformed soft bar. Such a method could be quite helpful in modeling the influence of plantations on sediment transport, which is important in environmental engineering.

(a) Re = 1

(b) Re = 1000

Fig. 1 Dynamical behavior of a soft bar in fluids with different Reynolds numbers

Besides, Prof. Galindo-Torres and his group try to simulate the behavior of the fish in the fluid. In Fig. 2, collaborating with Chair Prof. Cui Weicheng’s group studying robotic fish, Dr. Pei Zhang built a modeled fish and studied the drag force subjected to the fished in different Reynold number conditions. This coupling method can be widely applied to simulate submarine robots. Further, we can see its potential in medical science (e.g. simulating the deformation of eyeballs) and ergonomics (e.g. simulating the impact of water on the human body during platform diving).

(a) Modeled fish

(b) Modeling in different flow conditions

Flow and deposition of granular columns

Prof. Galindo-Torres and his group are also working on another fundamental topic related to granular materials. Geo-materials in nature and particulate materials in civil engineering and chemical engineering can all be regarded as granular materials. Granular systems, consisting of solid particles, often behave like solids when the solid fraction is sufficiently large, but can also behave like liquids when the system is loosely packed. The smooth transition of granular materials between solid-like behavior and liquid-like behavior makes it difficult for us to accurately describe the mechanical behavior of the assembly. Among problems related to granular materials, the collapse of granular columns has drawn continuous attention due to the potential link to the dynamics and deposition morphologies of various geophysical flows, such as landslides, debris flows, and pyroclastic flows. In Fig. 3, we can see that the morphology of Bora Bora island in the Pacific looks quite similar to the deposition morphology of a tall granular column.

Fig. 3 (a) Contour plot of the final deposition morphology of a tall granular column with a square cross-section (b) Satellite image of Bora-Bora island in French Polynesia (image acquired from the Internet)

In 2004, Prof. Herbert Huppert, a fellow of the Royal Society of the UK and professor at the University of Cambridge, and his colleagues investigated the dynamics and deposition of granular column collapses with laboratory experiments. However, on one hand, it is challenging to accurately control and measure the details of a lab test. On the other hand, the real interaction between particles is also missing from the analysis. In 2019, Herbert visited Westlake University during WISE2019 and shared his experience in studying fluid mechanics and granular materials. His interesting presentation became the starting point of the collaboration to study the behavior of granular column collapses with numerical methods.

Prof. Galindo-Torres has started to build up his own discrete element method modeling platform since around 2009. The modeling system can accurately simulate the behavior of granular assemblies in different loading and boundary conditions and obtain accurate contact forces between particles. Further, Prof. Galindo-Torres worked to establish the sphero-polyhedral particles model so that simulating the behavior of complex-shaped particles became possible.

Fig. 4 Spatial distribution of particle velocities during the granular column collapse, and the corresponding solid fraction distribution during the collapse.

In this work, Prof. Galindo-Torres’ group studied the influence of friction on the behavior of granular column collapses and quantitatively investigated how friction impacted the deposition morphology and the runout distance. When tall granular columns collapse, they tend to behave like liquids. Based on this work, we observed obvious size effects related to granular column collapses, thus, directly introducing test results obtained from laboratory experiments to real engineering problems with large scales might cause huge danger.

Thus, Prof. Galindo-Torres’ group applied the finite-size scaling (FSS) analysis, which is common in statistical physics, to the study of granular column collapses, and obtained a universal solution to describe the runout distance of granular columns with a wide range of system sizes. The above research is still a small fraction of current works of granular materials. Further study is needed to broaden our understanding of transient rheology of granular systems and/or granular-fluid systems and explore the potential of utilizing the granular rheology to predict and calculate real geophysical flows.

[1] Zhang, P., Sun, S., Chen, Y., Galindo-Torres, S. A., & Cui, W. (2021). Coupled material point Lattice Boltzmann method for modeling fluid–structure interactions with large deformations. Computer Methods in Applied Mechanics and Engineering, 385, 114040.  https://doi.org/10.1016/j.cma.2021.114040 

[2] Man, T., Huppert, H. E., Li, L., & Galindo-Torres, S. A. (2021). Finite-Size Analysis of the Collapse of Dry Granular Columns. Geophysical Research Letters, 48, e2021GL096054. https://doi.org/10.1029/2021GL096054