Fu Shuo said: "I know why the river changes its direction. Next, I would like to ask, is there any way to simulate the flow of water here?"
Dong Chu said, "Are you studying fluids?"
Fu Shuo said, "No, I study computers."
Dong Chu said: "The simulation of water flow is very difficult. There is a big difference between the simulated and actual water flow positions. Many factors are not taken into account, such as wind speed, obstruction by soil and stones, and surface tension."
The fluid macro model believes that fluid is continuously composed of countless fluid elements, that is, a continuous medium. The so-called fluid element refers to a small piece of fluid: its size is insignificant compared with the physical object placed in the fluid, but it is much larger than the mean free path of the molecules. It contains enough molecules to perform statistics. Macroscopic parameters are calculated on average, and a few molecules entering and exiting the fluid element will not affect the stable average value.
On the other hand, the time for statistical averaging should also be selected large enough so that during this period, microscopic properties, such as collisions between molecules, have been carried out many times, and statistical averaging during this period can obtain Stable value. Therefore, it is known from statistical physics that the physical quantities of molecules (mass, velocity, momentum and energy) are transformed into macroscopic physical quantities such as mass, velocity, pressure and temperature of fluid elements after statistical averaging, and inputs such as molecular mass, momentum and energy. The transport process, after statistical averaging, manifests itself as diffusion, viscosity, heat conduction and other macroscopic properties.
There are generally two ways to describe fluid motion.
Lagrangian method: In the Lagrangian method, the center of attention, that is, the focus, is the fluid particle, and the movement laws of all fluid particles are determined, that is, the law of how their positions change with time. It is very obvious that if the motion laws of all fluid particles are known, then the situation of the entire fluid motion will also be clear.
To express the viewpoints and methods of describing motion using mathematical formulas, we must first use some mathematical method to distinguish different fluid particles. The coordinates of the fluid particles at the initial moment are usually used as a symbol to distinguish different fluid particles. Assume that at the initial time t = t0, the coordinates of the fluid particle are a, b, c, which can be curved coordinates or rectangular coordinates.
Euler method: The Euler method does not directly consider how individual fluid particles move, but uses a field perspective to study fluid motion. It only focuses on the flow conditions that occur at a given point in space; where and how the fluid particles reach this point at a given moment, and where and how they move to other places after passing this point. Yes, all these issues are not fundamental from the Euler method point of view. In this way, the Euler method studies the velocity of a fluid particle at a fixed point (x, y, z) in space as a function of time.
Since the velocity functions determined by the above formula are defined on space points, they are functions of the space point coordinates x, y, z, so the fields studied are fields, such as velocity fields, etc. Therefore, when describing motion using the Euler perspective, the knowledge of field theory can be used.
Computational fluid dynamics is the analysis of systems containing related physical phenomena such as fluid flow and heat conduction through computer numerical calculations and image display. The basic idea can be summarized as follows: replace the original physical fields that are continuous in the time domain and space domain, such as the velocity field and pressure field, with a set of variable values at a series of finite discrete points, through certain principles and methods. A system of algebraic equations about the relationship between the field variables at these discrete points is established, and then the system of algebraic equations is solved to obtain approximations of the field variables. It can be seen as a numerical simulation of flow under the control of the basic equations of flow (mass conservation equation, momentum conservation equation, energy conservation equation).
Dong Chu said: "I think that for rivers, it can be simulated like this. There are several steps."
"1. Establish a river model: Use process simulation software to establish a three-dimensional model of the river, including the river channel, river bed, water surface and surrounding environment. You can use modeling tools to create river models, or you can import river models from other software. 2. Define water droplets: Define parameters such as mass, volume, density and movement speed of water droplets, and place water droplets in the river. 3. Set force fields: Set various force fields in the river, such as gravity, inertial force, buoyancy and resistance, etc. , to describe the effects of various forces on water droplets in the river. 4. Run simulation: Run the process simulation software to observe the movement and force of the water droplets in the river. The movement of the water droplets can be displayed through the visualization tools in the software Trajectory and force conditions. 5. Analysis results: Analyze the movement patterns and characteristics of water droplets in the river based on the simulation results, such as the speed, acceleration, flow path and residence time of water droplets. The model and force field can be further optimized to improve simulation Accuracy and reliability of results.”
Fu Shuo said: "But the running process of water is very complicated. How to take all situations into consideration?"
Zhan Guyue thought for a while and said, "What if all the water cycle processes were enumerated."
The cycle of water droplets on the Earth includes evaporation, condensation, precipitation and surface runoff.
Evaporation: Solar energy irradiates water bodies on the surface of the earth such as oceans, rivers, lakes, reservoirs, etc., causing water molecules on the surface of the water bodies to transform into gaseous water vapor, thereby entering the atmosphere.
Condensation: After water vapor rises in the atmosphere, it encounters cold air. The water vapor will quickly reduce its temperature and condense into small water droplets, forming clouds.
Precipitation: Water droplets in clouds continue to condense and grow. When the water droplets become large enough, precipitation in the form of rain or snow will fall. Part of the precipitation will flow into rivers, lakes, reservoirs and other water bodies.
Surface runoff: Part of the precipitation will seep into the ground, causing soil, rocks, etc. to form underground water layers, and seep out of the ground called surface runoff, mainly flowing into the ocean.
The above process constitutes the water cycle on the earth, and water forms an ecological cycle system on the earth that is constantly transformed and updated.
Dong Chu said: "I think you just like to use stupid methods, enumeration methods."
Fu Shuo said: "On this basis, the plan can be further improved. Various movements of water can be simulated, then measured, compared with the simulated values, and then the simulation program can be modified."
"We can actually measure these and then use the computing network to try it out," Zhanguyue said.
Dong Chu said: "But the most difficult thing is how to measure the actual state of the water droplets, including flow rate, pressure, temperature, etc."
Zhan Guyue said: "I think the macroscopic water flow can still be detected."
