On the implementation of an adaptive multirate framework for coupled transport and flow

TL;DR

This paper develops an adaptive multirate time-stepping framework for coupled transport and flow problems, utilizing goal-oriented error control with the Dual Weighted Residual method and discontinuous Galerkin discretization.

Contribution

It introduces a novel multirate in time approach with goal-oriented adaptivity for coupled transport and flow, including a new error representation and implementation strategies.

Findings

Effective separation of temporal and spatial errors for adaptive refinement

Successful numerical convergence demonstrating the method's accuracy

Application to convection-dominated transport problems shows practical relevance

Abstract

In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual (DWR) method. Key ingredients are an arbitrary degree discontinuous Galerkin time discretization of the underlying subproblems, an a posteriori error representation for the transport problem coupled with flow and its implementation using space-time tensor-product spaces. The error representation allows the separation of the temporal and spatial discretization error which serve as local error indicators for adaptive mesh refinement. The performance of the approach and its software implementation are studied by numerical convergence examples as well as an example of physical interest for convection-dominated transport.