According to the properties of variables contained in the model, mathematical models describing groundwater movement can be divided into two categories.

1) Deterministic model: variables in the model take certain values.

2) Stochastic model: the variables in the model are random, and only the probability of the variables is known, but the definite value of the variables cannot be determined.

Groundwater dynamics mainly studies deterministic models.

deterministic model

Include partial differential equations and definite solution conditions.

1. partial differential equation

Also known as the governing equation describing groundwater movement. According to the law of conservation of mass and energy conversion, it is an equation satisfied by the depth of groundwater head or water level drop, which reflects the universal law of groundwater movement.

2. Definite solution conditions

1) boundary condition: refers to the hydraulic properties on the geometric boundary of seepage area. Usually divided into the first kind of boundary and the second kind of boundary. The first boundary (given head boundary), if the water level of rivers and reservoirs is taken as the boundary value, the non-disappearing overflow zone is also a boundary, and its ground elevation can be taken as the boundary value; The second kind of boundary (given flow boundary), such as shaft wall, water blocking fault and underground watershed, the latter two are zero flow boundaries.

2) Initial conditions: For unsteady flow, in addition to the above boundary conditions, there must also be initial conditions, that is, the head distribution in a given seepage area at a certain moment, indicating the state of starting to study the unsteady flow process. The "a certain moment" mentioned here is a relative moment, which is usually considered as zero moment, that is, t=0.