# Application of Physics-Informed Neural Networks to River Sifting Simulation
## 3 Results
### Numerical Result from ANSYS  
This study aims to model the problem of the Sod shock tube. The task is to simulate the propagation of a normal shock wave inside a shock tube under experimental conditions. The obtained numerical results are compared with the results obtained using the PINN method, which is a widely popular method in fluid flow simulation. To check the correctness and accuracy of the mathematical model used, the test problem was solved numerically, based on the research of other authors. For this, a 2D shock tube model was used, which is a long metal tube consisting of two chambers and separated by a diaphragm. The diaphragm separates the high-pressure area from the low-pressure area. After the diaphragm is removed, the shock wave and the contact discontinuity begin to move to the region of initially low pressure, and the rarefaction wave moves to the region of initially high pressure ([PERSON] et al., 2013, [38]). Two different solvers were used in the problem: driver and driven. The chamber used consists of two gases with a high-pressure ratio. Thus, one chamber is filled with high-pressure ideal gas, the driver, and the other chamber, vice versa, is low-pressure, and is called the driven. A schematic representation of the studied reservoir is shown in Figure 7. The length of this reservoir is \(\mathrm{L_{b}}\) = 1 m and \(\mathrm{H_{b}}\) = 0.03 m. When modeling, a piercing mechanism was built into the diaphragm, which breaks the diaphragm under given conditions. When the contact is suddenly broken, a series of pressure waves are created that cause a shock wave. The computational grid plays a fundamental role in ensuring accuracy and detail when conducting calculations using the PINN and Ansys methods. It enables more precise and detailed modeling of physical phenomena, ultimately leading to more reliable results and a deeper understanding of the processes under study. Therefore, for this task, a structured computational mesh was used, the total number of elements of which was 30,000, and the number of nodes was 31,031. Face meshing = \(1\times 10^{-3}\) m. The total duration of the task calculation is 3000 time steps. The initial conditions for the test problem for Ansys are presented in Figure 8.  
The obtained numerical results were compared with the results obtained by using the PINN method. As can be seen, the numerical simulation results show exact solutions to the problem with a clear shock effect. In solving the problem using PINN, the shock effect is not explicitly shown. The obtained numerical results were compared with the results obtained using the PINN method at different time intervals, and these results were compared. As can be seen,  
Figure 8: Initial conditions for the test problem. Figure 7: Geometry of the test problem. numerical modeling provides accurate solutions to this problem, displaying the clear effect of shock waves. When solving the same problem using the PINN method, the shock wave effect is not explicitly highlighted. This difference in results can be explained by the fact that the PINN method employs artificial neural networks to solve physical problems. In this method, neural networks are trained to integrate physical laws and conditions into the solution process. Thus, the PINN method strives to create smooth and continuous solutions, which may not clearly represent explicit physical effects, such as shock waves, in the results. In numerical modeling, on the other hand, problems are solved using numerical methods that can more accurately capture physical phenomena, such as shock waves. These methods discretize the space into a grid and solve equations on each grid element, allowing for a more detailed description of physical processes. Therefore, comparing numerical results with the results obtained using the PINN method allows for the identification of differences in approaches and the advantages of each method.