NavierStokesBerechnungen

Navier-Stokes Equations are a set of nonlinear partial differential equations that describe the motion of fluids, such as liquids and gases. These equations are named after Claude-Louis Navier, a French mathematician, and George Gabriel Stokes, an Irish physicist, who independently developed the equations in the 19th century. The Navier-Stokes Equations are a fundamental concept in fluid dynamics and are used to study a wide range of phenomena, including ocean currents, atmospheric circulation, and the behavior of viscous fluids in various engineering and scientific applications.

The Navier-Stokes Equations describe the motion of a fluid by considering the balance between the forces acting on the fluid and the resulting motion. The equations account for the effects of viscosity, pressure, and inertia on the fluid, and they are nonlinear, meaning that the equation's behavior changes depending on the fluid's velocity. In the equations, the Navier Number (Re) represents the ratio of inertia to viscosity forces and is used to characterize the fluid's behavior based on its flow characteristics.

The Navier-Stokes Equations are given by three scalar equations that account for the conservation of mass, momentum, and energy in the fluid. The first equation is the continuity (or mass conservation) equation, which states that the rate of change of mass within a control volume is equal to the mass flux through the control surface. The second and third equations describe the conservation of momentum and are coupled through the velocity field. Due to their nonlinearity, the Navier-Stokes Equations have been recognized as a crucial mathematical challenge to identify turbulent flow regimes and provide accurate solutions that effectively capture real-world fluid dynamics phenomena.