Some practical versions of boundary variation diminishing (BVD) algorithm

TL;DR

This paper introduces practical variants of the boundary variation diminishing (BVD) algorithm, demonstrating their simplicity and effectiveness for linear advection and potential for multi-dimensional applications.

Contribution

It presents new variant schemes of the BVD algorithm with numerical results, enhancing practical implementation for linear and nonlinear equations.

Findings

Variants show improved numerical stability

Schemes are easy to implement in multi-dimensions

Effective for linear advection equations

Abstract

This short note presents some variant schemes of boundary variation diminishing (BVD) algorithm in one dimension with the results of numerical tests for linear advection equation to facilitate practical use. In spite of being presented in 1D fashion, all the schemes are simple and easy to implement in multi-dimensions on structured and unstructured grids for nonlinear and system equations.