Factuté des Sciences et Techniques
Université Marien Ngouabi
BP 69 Brazzaville,
Congo.
E-mail: bienvenu.ondami@umng.cg 

Abstract:

We present a comprehensive numerical study of direct simulation for second order hyperbolic equations with highly oscillatory coefficients. The focus is on regimes where classical homogenization either breaks down or provides unreliable approximations for practical computations. A robust finite volume spatial discretization combined with a fourth order Runge--Kutta time integration method is used to construct a systematic numerical atlas over a wide range of scale separation parameters.
The study compares the behavior of direct numerical simulation and homogenized models in regimes where the microscopic scale is well separated from the macroscopic one, in intermediate regimes where this separation deteriorates, and in situations where fine scale features remain physically relevant. Particular attention is paid to the occurrence of numerical locking in finite volume schemes when critical relations between mesh size and microscopic scale are met.
The results provide practical guidelines for mesh design, identification of reliable parameter ranges for homogenized models, and detection of numerical artefacts. The work highlights the complementarity, rather than the competition, between asymptotic homogenization and direct numerical simulation for multiscale modeling of hyperbolic problems.

Full Text PDF: