Convergence Analysis of a Class of Massively Parallel Direction Splitting Algorithms for the Navier-Stokes Equations

TL;DR

This paper presents a convergence analysis of a new direction splitting algorithm for the Navier-Stokes equations, highlighting its stability, efficiency, and suitability for parallel computing.

Contribution

It introduces a novel fractional time-stepping method that is unconditionally stable, convergent, and optimized for parallel implementation.

Findings

Algorithm is linearly complex

Proven to be unconditionally stable

Suitable for massive parallelization

Abstract

We provide a convergence analysis for a new fractional time-stepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization.