# Generating boundary conditions for a Boussinesq system

## TL;DR

This paper introduces a novel numerical method for implementing boundary conditions in a 1D Boussinesq system, effectively handling dispersive boundary layers without increasing computational cost.

## Contribution

A new reformulation-based approach for generating boundary conditions in Boussinesq systems that avoids additional computational overhead.

## Key findings

- Method accurately handles dispersive boundary layers.
- Validated through multiple numerical simulations.
- No increase in computational time compared to periodic boundaries.

## Abstract

We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer that is created at the boundary when the boundary conditions are non homogeneous. This method is implemented for a simple first order finite volume scheme and validated by several numerical simulations. Contrary to the other techniques that can be found in the literature, our approach does not cause any increase in computational time with respect to periodic boundary conditions.