Fluidbereich

Fluidbereich, literally "fluid region" in German, denotes the region of space in which a fluid is present for a given problem and within which the fluid’s properties and motion are described. It is the domain over which the governing equations of fluid dynamics are applied, and it may be fixed or time-dependent.

In most classical formulations, the Fluidbereich is governed by the Navier-Stokes equations for momentum balance, together with the continuity equation for mass conservation. For compressible flows, energy conservation and state equations are also included. The specific constitutive relations depend on the fluid model, such as Newtonian or non-Newtonian behavior, and on whether thermal effects are considered.

Boundaries of the Fluidbereich are crucial for problem setup. They can be solid walls with no-slip or slip boundary conditions, free surfaces with atmospheric pressure, or interfaces between immiscible fluids where velocity continuity and stress balance are enforced. In problems with moving boundaries or deformable domains, the Fluidbereich itself evolves in time as the geometry changes, as in blood flow in compliant vessels or free-surface flows like waves on water.

In computational fluid dynamics, the Fluidbereich is discretized into a mesh or grid. Numerical methods, such as finite element, finite volume, or finite difference schemes, solve the governing equations within the discretized domain while applying appropriate boundary conditions on its boundary.

Applications include pipe and channel flows, aerodynamics around bodies, hydrodynamics of ships and offshore structures, and physiological flows in the cardiovascular system. The concept also underpins multiphase and free-surface flow analyses where domains may change with time.