Staggered grids for multidimensional multiscale modelling

• Published in: Computers & fluids 2024-03, Vol.271, p.106167, Article 106167
• Main Authors: Divahar, J., Roberts, A.J., Mattner, Trent W., Bunder, J.E., Kevrekidis, Ioannis G.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Equation-free patch scheme; Large-scale waves; Multiscale modelling; Staggered grids
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2023.106167

For high accuracy and to improve simulated wave characteristics, this article extends the concept of staggered grids to novel multidimensional multiscale modelling enabling efficient computation on sparse patches. Computational schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence simulations of wave-like systems lacking proper handling of these numerical issues often fail to represent the physical characteristics of wave phenomena. This challenge gets even more intricate for multiscale modelling, especially in multiple dimensions. But numerical schemes on staggered grids are significantly less dispersive, better model the group velocity, and preserve much of the wave characteristics. This article develops and exhaustively studies all 167040 possible 2D multiscale staggered grids. Our catalog (Divahar, 2023) interactively plots all of them. Only 120 multiscale staggered patch grids give stable and accurate multiscale schemes. Specifically, this article develops these 120 multiscale staggered grids and demonstrates their stability, accuracy, and wave-preserving characteristic for equation-free multiscale modelling of weakly damped linear waves. These characteristics of the developed multiscale staggered grids must also hold in general for multiscale modelling of many complex spatio-temporal physical phenomena such as the general computational fluid dynamics. •We develop and comprehensively explore multidimensional multiscale staggered grids.•Among 167040 2D multiscale staggered grids, only 120 give stable and accurate schemes.•These 120 grids give highly accurate equation-free multiscale patch scheme for waves.•We show the accuracy for multiscale modelling of ideal and weakly damped linear waves.•This work provides an essential foundation to multiscale schemes for wave systems.