The ultimate goal in computational fluid dynamics is to obtain desired solutions as accurately as possible while minimizing the requirement for computational resources. Thus, we ask: how do we achieve both “accuracy” and “efficiency” at the same time? Often we exercise a compromise where we may choose to sacrifice some accuracy for the sake of expediting a solution, or vice versa. Does an acceptable compromise exist? These are the types of questions that typically enter the minds of the CFD practitioner before undertaking a major project.

Given a fixed computational method and limited computer resources, one is confronted with a decision as to which direction to follow. The most feasible approach under these restricted circumstances will be to seek the best computational grid arrangement which will lend itself to the best possible accuracy and maximum efficiency. Adaptive methods are designed to achieve both accuracy and efficiency, with mesh refinements provided selectively only where needed.