2013/12/30 by J. E. Bunder, Bunder, J. E., A. J. Roberts +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Lattice Boltzmann Simulation Studies
paper · pdf · doi:10.48550/arxiv.1312.7638
openalex publication_date 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements empowers the approach to resolve significant subgrid microscale structures and interactions between neighbouring elements. The crucial aspect of this approach is that centre manifold theory organises the resolution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements. The techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differential\difference equations, such as the forced Burgers' equation, adopted here as an illustrative example.