Ensemble algorithm for parametrized flow problems with energy stable open boundary conditions

TL;DR

This paper introduces energy-stable ensemble algorithms for parametrized Navier-Stokes flow problems with open boundary conditions, enabling efficient simulations under varying parameters while maintaining stability.

Contribution

It extends ensemble methods to open boundary conditions with proven energy stability, requiring only one system solve with multiple right-hand sides.

Findings

Proved stability under CFL condition involving velocity fluctuations

Developed schemes requiring a single system solve with multiple RHS

Extended ensemble methods to open boundary conditions with energy stability

Abstract

We propose novel ensemble calculation methods for Navier-Stokes equations subject to various initial conditions, forcing terms and viscosity coefficients. We establish the stability of the schemes under a CFL condition involving velocity fluctuations. Similar to related works, the schemes require solution of a single system with multiple right-hand sides. Moreover, we extend the ensemble calculation method to problems with open boundary conditions, with provable energy stability.