Nivåsetmetoden

Nivåsetmetoden, which translates to "level-setting method," is a numerical technique used in computational fluid dynamics (CFD) and other fields involving interface tracking. It is primarily employed to represent and evolve a sharp interface between two or more immiscible fluids or phases. The core idea is to maintain a smooth, continuous function, often called the level-set function, that implicitly defines the interface.

The level-set function, denoted by $\phi$, is defined such that its zero contour ($\phi = 0$) represents the interface. Typically, $\phi$ is assigned positive values on one side of the interface and negative values on the other. The sign of $\phi$ indicates which fluid is present, while the magnitude of $\phi$ often represents the signed distance to the nearest point on the interface. This distance property is important for certain operations and numerical schemes.

The evolution of the interface over time is governed by the advection of the level-set function. This is typically achieved by solving a partial differential equation, often a conservation equation like $\frac{\partial \phi}{\partial t} + \mathbf{u} \cdot \nabla \phi = 0$, where $\mathbf{u}$ is the velocity field. Numerically, this equation is solved using various discretization schemes, such as finite differences or finite volumes, ensuring that the interface is accurately propagated.

A key challenge with the basic level-set method is that the signed distance property can be lost over time due to numerical diffusion and discretization errors. To counteract this, reinitialization procedures are periodically applied. Reinitialization ensures that $\phi$ remains a true signed distance function, which is crucial for accurate surface tension calculations and other geometric operations. Despite its advantages in handling complex interface topologies, such as breaking and merging, the level-set method can suffer from mass conservation errors, which may require specific treatments or coupling with other methods for strict conservation.