10
P. Liu
This method of staring at particles (which can be visually seen as the
working way of “police tracking thieves”) is a direct extension of the particle
system method in theoretical mechanics. The reason is that it is a concept
extension. Here, it refers to countless continuous particle systems, where it
refers to countable discrete particle systems. Whether this extension from
individual to general concepts is feasible or not is worth studying mathematically. This method is clear in concept and convenient for the direct
generalization of physical laws. However, the disadvantage is that there are too
many records, especially for the flow characteristics of only local areas, which
is very inconvenient. For example, in the flood season every year, people only
want to know the water regime of the Yangtze River in the Wuhan section
(the water level at Wuhan Pass), but when using this method to describe it,
we must make clear the origin of all water quality points passing through the
Yangtze River in Wuhan section, track and record the flow process of each
particle throughout the whole process, so as to depict the flow characteristics
of the Yangtze River in Wuhan section. In fact, it is useless for many records
of water quality points in the Yangtze River which are not located in the
Wuhan section.
2. Euler Method
This method is also called the space point method or the flow field method.
In order to avoid unnecessary data recording by the Lagrange method, Euler
proposed that instead of identifying fluid particles, he changed the space
points to identify the flow area (the relationship between space points and
particles still satisfies the continuity hypothesis). The observer remained
stationary relative to space points and recorded the speed of different particles
passing through fixed space points at different times. The amount directly
recorded by the observer is the particle velocity value passing through the
space point at different times. For example, arranging an observer at each
space point and recording the particle velocity value of each space point at
each time can give a comprehensive understanding of the characteristics of
the flow area investigated. Please note that although this method identifies
spatial points, it still studies fluid particles, so it can be said that it is an unlabeled particle system method. For example, for any space point in the region
under investigation, the velocity of fluid particles passing through the space
point is directly recorded at time t as u (x, y, z, t ), v (x, y, z, t ), and w (x, y,
z, t ). If the velocity of particles passing through all spatial points in the flow
region is recorded, the flow field at any time in the region can be understood.
This method does not need to identify the fluid particle information, but
P. Liu
This method of staring at particles (which can be visually seen as the
working way of “police tracking thieves”) is a direct extension of the particle
system method in theoretical mechanics. The reason is that it is a concept
extension. Here, it refers to countless continuous particle systems, where it
refers to countable discrete particle systems. Whether this extension from
individual to general concepts is feasible or not is worth studying mathematically. This method is clear in concept and convenient for the direct
generalization of physical laws. However, the disadvantage is that there are too
many records, especially for the flow characteristics of only local areas, which
is very inconvenient. For example, in the flood season every year, people only
want to know the water regime of the Yangtze River in the Wuhan section
(the water level at Wuhan Pass), but when using this method to describe it,
we must make clear the origin of all water quality points passing through the
Yangtze River in Wuhan section, track and record the flow process of each
particle throughout the whole process, so as to depict the flow characteristics
of the Yangtze River in Wuhan section. In fact, it is useless for many records
of water quality points in the Yangtze River which are not located in the
Wuhan section.
2. Euler Method
This method is also called the space point method or the flow field method.
In order to avoid unnecessary data recording by the Lagrange method, Euler
proposed that instead of identifying fluid particles, he changed the space
points to identify the flow area (the relationship between space points and
particles still satisfies the continuity hypothesis). The observer remained
stationary relative to space points and recorded the speed of different particles
passing through fixed space points at different times. The amount directly
recorded by the observer is the particle velocity value passing through the
space point at different times. For example, arranging an observer at each
space point and recording the particle velocity value of each space point at
each time can give a comprehensive understanding of the characteristics of
the flow area investigated. Please note that although this method identifies
spatial points, it still studies fluid particles, so it can be said that it is an unlabeled particle system method. For example, for any space point in the region
under investigation, the velocity of fluid particles passing through the space
point is directly recorded at time t as u (x, y, z, t ), v (x, y, z, t ), and w (x, y,
z, t ). If the velocity of particles passing through all spatial points in the flow
region is recorded, the flow field at any time in the region can be understood.
This method does not need to identify the fluid particle information, but