The purpose of the relaxation of high order terms is to improve the startup and the general solution
behavior of flow simulations when higher order spatial discretizations are used (higher than first). It has also shown to prevent convergence stalling in some cases. Such high-order terms can be of significant importance in certain cases and lead to numerical instabilities. This is particularly true at aggressive solution settings. In such cases, high order relaxation is a useful strategy to minimize your interaction during the solution. This can be an effective alternative to starting the solution first order, then switching to second order spatial discretization at a later stage.