Physics

Asymptotic analysis

Mathematics

Statistical physics

Mathematical analysis

Kinetic energy

Kinetic theory

Scale (ratio)

Theoretical physics

Computer science

Quantum mechanics

Applied mathematics

Classical mechanics

Statistical mechanics

Acta Numerica

We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the asymptotic-preserving (AP) strategies to compute multiscale physical problems efficiently. Specifically, we will first study the asymptotic transition from quantum to classical mechanics, from classical mechanics to kinetic theory, and then from kinetic theory to hydrodynamics. We then review some representative AP schemes that mimic these asymptotic transitions at the discrete level, and hence can be used crossing scales and, in particular, capture the macroscopic behaviour without resolving the microscopic physical scale numerically.

Asymptotic-preserving schemes for multiscale physical problems