On monolithic and Chorin–Temam schemes for incompressible flows in moving domains

Reidmen Aróstica,Cristóbal Bertoglio

doi:10.1016/j.aml.2020.106830

Abstract

Several time discretization schemes for the incompressible Navier–Stokes equations (iNSE) in moving domains have been proposed. Here we introduce them in a unified fashion, allowing a common well posedness and time stability analysis. It can be therefore shown that only a particular choice of the numerical scheme ensures such properties. The analysis is performed for monolithic and Chorin–Temam schemes. Results are supported by numerical experiments.

Highlights

Several works have been reported dealing with the numerical solution of the incompressible Navier-Stokes equations (iNSE) in moving domains within an Arbitrary Lagrangian Eulerian formulation (ALE), primarily in the context of fluid-solid coupling
We describe a family of Chorin-Temam (CT) schemes for the iNSE-ALE problem, as we did for the monolithic case
The stability analysis is confirmed by numerical experiments

Summary

Introduction

Several works have been reported dealing with the numerical solution of the iNSE in moving domains within an Arbitrary Lagrangian Eulerian formulation (ALE), primarily in the context of fluid-solid coupling. To the best of the authors knowledge, only a few monolithic schemes have been thoroughly analyzed, e.g. in [4, 14, 17, 19], while no analysis has been reported for Chorin-Temam (CT) methods. The goal of this work is to assess well-posedness and unconditional energy balance of the iNSE-ALE for all reported monolithic and CT discretization schemes within a single formulation.

The continuous problem

Chorin-Temam schemes

Numerical examples

Conclusion