Equation-free multiscale staggered patch schemes - a step towards transformative multiscale CFD
Channel: jdivahar
Date: 2023-01-22

This is an invited talk delivered by J. Divahar [https://www.linkedin.com/in/jdivahar] on 12th January 2023 in the ICME Seminar Series 2023 at Tata Research Development and Design Centre (TRDDC), Pune, India.

The equation-free multiscale modelling methods are a very young and active area of research. So, the structure of the talk is centred around their simplified introduction with several examples and illustrations.

Divahar is a postdoctoral researcher in applied mathematics at The University of Adelaide, South Australia.  He develops and analyses accurate and efficient multiscale numerical schemes for fluid flows.

Abstract: Many physical phenomena exhibit complex multiscale, nonlinear, emergent behaviour (e.g., turbulent flows, combustion, large-scale waves in the atmosphere and oceans).  Generally, the main interest is only in the large-scale (coarse-scale) dynamics (e.g., mean flow), yet the effect of much smaller scales (fine-scale) that dominantly influence the emergent coarse-scale dynamics needs to be accounted for.  This leads to very many state variables and prohibitively high computational costs.  Many multiscale modelling methods aim to address this issue.  Equation-free patch scheme (Kevrekidis et al. 2009, e.g.) is a flexible, computationally efficient, multiscale modelling approach that is very successful for dissipative systems.  But for waves and flows with negligible dissipation (hyperbolic systems), the challenges of numerical dissipation and dispersion get much more intricate for multiscale modelling, especially in multiple dimensions.  So, invoking modern dynamical systems theory, Divahar (2022) has developed equation-free multidimensional multiscale (reduced-order) staggered patch schemes.  These schemes remarkably reduce compute times by about 100,000 times compared to the same-resolution full-domain simulation for linear waves.  Computational complexity studies promise an even larger computational advantage for complex nonlinear flows.  This extensive and fundamental work opens up many opportunities for efficient and accurate multiscale simulation of complex nonlinear waves and flows.  In this talk, Divahar will discuss his recent work on multiscale staggered patch grids and schemes.  He will also briefly touch upon their potential for transformative new algorithms in computational fluid dynamics (CFD).

Related publications.
Article 1: Large-scale simulation of shallow water waves via computation only on small staggered patches, https://doi.org/10.1002/fld.4915 (https://doi.org/10.48550/arXiv.1912.07815).
Article 2: Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves, https://doi.org/10.1016/j.cma.2023.116133 (https://doi.org/10.48550/arXiv.2210.15823).
Article 3: Staggered grids for multidimensional multiscale modelling, https://doi.org/10.1016/j.compfluid.2023.106167  .
Thesis: Accurate multiscale simulation of wave-like systems, https://digital.library.adelaide.edu.au/dspace/handle/2440/136347  .