Multicontinuum homogenization and its relation to nonlocal multicontinuum theories.

In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing boundary effects. We discuss different choices of constraints for cell problems. We present numerical results that show how oversampling reduces boundary effects. Finally, we discuss the relation of the proposed methods to our previously developed methods, Nonlocal Multicontinuum Approaches. • We derive multicontinuum methods using a homogenization-like expansion and present constraint cell problem formulations. • Constraint cell problems allow using averages for different continua and give a flexibility to the framework. • We discuss appropriate local boundary conditions in representative volume elements and introduce oversampling. • The resulting multicontinuum equations show that local averages of the solution will differ among each other. • The average constraints, discussed in this paper, are easy to set and guarantee exponential decay. [ABSTRACT FROM AUTHOR]