On the use of slow manifolds in molecular and geophysical fluid dynamics

Abstract

Constraints typically arise from the elimination of high frequency oscillations in mechanical systems. Examples are provided by bond constraints in molecular simulations and incompressibility constraints in fluid dynamics. A key issue is the accuracy of constrained dynamics with regard to the full dynamics. In this review we focus on the smooth solution components and discuss the concept of slow manifold and soft constraints in molecular and geophysical fluid dynamics. While the formal mathematical derivation of constraints is the same for both molecular and fluid dynamics, the predominant numerical techniques for dealing with constraints are different in the two fields. Semi-implicit time- stepping methods are often used in geophysical fluid dynamics while explicitly enforced constraints are more common in molecular dynamics.