Boundary Conditions – Pressure

The ability to specify a pressure condition at one or more boundaries of a computational region is an important and useful computational tool. Pressure boundaries represent such things as confined reservoirs of fluid, ambient laboratory conditions, and applied pressures arising from mechanical devices.

Generally, a pressure condition cannot be used at a boundary where velocities are also specified, because velocities are influenced by pressure gradients. The only exception is when pressures are necessary to specify the fluid properties, e.g., density crossing a boundary through an equation of state.

Types of Pressure Boundary Conditions

There are typically two types of pressure boundary conditions, referred to as static or stagnation pressure conditions. In a static condition the pressure is more or less continuous across the boundary, and the velocity at the boundary is assigned a value based on a zero normal-derivative condition across the boundary.

In contrast, a stagnation pressure condition assumes stagnation conditions outside the boundary so that the velocity at the boundary is zero. This assumption requires a pressure drop across the boundary for flow to enter the computational region.

Since the static pressure condition assumes only that the normal fluid velocity at the boundary has a zero gradient, it is less specific than the stagnation pressure condition. In this sense the stagnation pressure condition is generally more physical and is recommended for most applications.

Pressure Boundary Example

For example, consider the problem of flow in a section of pipe. On the one hand, if the upstream end of the computational region coincides with the physical entrance to the pipe then a stagnation condition should be used to represent the external ambient conditions as a large reservoir of stationary fluid. On the other hand, if the upstream boundary of the computing region is inside the pipe, and many diameters away from the entrance, then the static pressure condition would be a more reasonable approximation to flow conditions at that location.