Some practical versions of boundary variation diminishing (BVD) algorithm
For computational fluid dynamics practitioners, it offers incremental improvements to the BVD method for better shock-capturing.
This note presents practical variants of the BVD algorithm for 1D linear advection, achieving improved accuracy and reduced dissipation in numerical tests. The schemes are designed for easy extension to multi-dimensional and nonlinear problems.
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.