Antidiffusive

Antidiffusive refers to a class of numerical methods used in computational fluid dynamics and other fields of scientific computing to mitigate the effects of numerical diffusion. Numerical diffusion is an artificial spreading of a quantity, such as a concentration or a velocity, that occurs due to the discretization of partial differential equations. This spreading can lead to inaccurate results, especially in regions with sharp gradients or discontinuities.

Antidiffusive methods aim to reduce or eliminate this numerical diffusion by introducing additional terms or corrections to the standard discretization schemes. These methods can be broadly categorized into two main types: flux-corrected transport (FCT) and essentially non-oscillatory (ENO) schemes. FCT methods modify the numerical fluxes to ensure that the solution remains bounded and does not exhibit spurious oscillations. ENO schemes, on the other hand, adaptively choose the stencil for the discretization based on the smoothness of the solution, thereby reducing numerical diffusion in smooth regions while maintaining sharp resolution in regions with discontinuities.

The development of antidiffusive methods has been driven by the need for accurate and efficient simulations of complex fluid flows, such as those encountered in aerodynamics, meteorology, and astrophysics. These methods have significantly improved the accuracy and reliability of numerical simulations, making them an essential tool in modern computational science.