Large-scale simulation of shallow water waves with computation only on small staggered patches

TL;DR

This paper extends a multiscale patch scheme to simulate shallow water wave systems on staggered grids in 2D, enabling efficient large-scale simulations by coupling small micro-scale patches with high-order consistency.

Contribution

It generalizes the patch scheme to 2D staggered grids for wave systems, providing a high-order, efficient multiscale simulation framework.

Findings

Enables large-scale wave simulations with reduced computational cost.

Achieves high-order consistency through macro-scale interpolation.

Successfully applied to turbulent shallow water models.

Abstract

The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings in computational time are possible. Here we discuss generalising the patch scheme to the case of wave systems on staggered grids in 2D space. Classic macro-scale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the emergent macro-scale simulation and the underlying micro-scale dynamics. Eigen-analysis indicates that the resultant scheme empowers feasible computation of large macro-scale simulations of wave systems even with complicated underlying physics. As examples we use the scheme to simulate some wave scenarios via a turbulent shallow water model.