Optimal Boundary Discretization by Variational Data Assimilation

TL;DR

This paper presents a variational data assimilation method to optimize boundary discretization in a linear shallow water model, improving accuracy by correcting boundary-related numerical errors.

Contribution

It introduces a novel approach to optimize boundary discretization operators using data assimilation, enhancing model accuracy without changing boundary conditions.

Findings

Optimized boundary discretization reduces boundary layer errors.

Data assimilation corrects wave velocity inaccuracies.

Method improves coarse grid model performance.

Abstract

Variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near boundary rather than boundary conditions is shown. Assimilating data produced by the same model on a finer grid in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under-resolved boundary layer and wrong wave velocity.