# Research Progress and Engineering Applications of Viscous Fluid Mechanics
## 2 Advances in the Study of the State of Motion of Viscous Fluids
### Experimentation and Research
#### 2.2.1 Computerized Algorithmic Solution of Viscous Fluids  
Currently, many scientists use computers to compile algorithmic programs to help them find the relationship between various variables from the huge amount of experimental data and at the same time set the program to iterate autonomously through the computer, and the computational speed far exceeds that of the original handwritten calculations. [PERSON] et al. [93] proposed an oscillatory flow condition relevant to marine applications based on the Navier-Stokes equation. A two-dimensional viscous flow field model for porous-plate hydrodynamics was developed and analytically solved using MATLAB, and the accuracy of the model was experimentally verified. [PERSON] et al. [94] investigated the particulate system of solid particles suspended in a viscoelastic medium based on a novel numerical algorithm of the lattice Boltzmann method (LBM). [PERSON] et al. [95] used the Giesekus model of viscoelastic fluid and spherical rigid particles as the research object and used the quasi-constant algorithm based on the relative motion model to investigate the distribution characteristics of the lateral lift force of the particles in the channel; the computational model is shown in Figure 12.  
[PERSON] et al. [96], for Oldroyd-B-type viscoelastic fluid, used the lattice Boltzmann method (LBM) to obtain the flow field distributions of the viscoelastic fluid in the dilatational and constrictive flow paths (the flow paths are shown in Figure 13) and numerically analyzed the settling process and characterization of the particles in dilatational and constrictive flows based on the point-source particle model.  
Figure 12: Schematic diagram of calculation model. In the figure, a single spherical particle moves in a square straight tube with a section side length H. In a fixed coordinate system O \(-\)XYZ, the flow field is unsteady. When the particle moves to a stable state driven by the fluid, its translation velocity and rotation velocity remain unchanged. When the relative motion model is used, the particles are placed in several transverse positions of the channel section, and the coordinate system o \(-\)xyz is established with the geometric center of the particles as the origin, and the particles are translated at the same speed. In this translation coordinate system o \(-\)xyz, the particle motion can be regarded as having only rotation velocity and no translation velocity; the movement velocity of the channel wall and the particle translation velocity are reversed. In the translational coordinate system o \(-\)xyz, the whole flow field is transformed into a fixed boundary and relatively steady flow, which can be solved numerically by using a fixed grid [95].  
Different from the forward algorithm which is based on using known conditions to obtain unknown results, [PERSON], IA, [97], with the final state of the target fluid being highly viscous and incompressible, used algorithms to deduce the unknown initial state of the fluid in reverse, using OpenFOAM software based on linear algebra to develop a new iterative algorithm in reverse, with the computational error and input data error on the opposite side. [PERSON], [PERSON], et al. [98] improved the SPH algorithm in order to simulate the transient free-surface flow of viscous and viscoelastic fluids, which improved the accuracy and stability of the algorithm. It can accurately and stably simulate the flow and oscillating pressure field at the free surface of viscous and viscoelastic fluids, which provides a more efficient method for the study of numerical algorithms for viscous fluids.