A Cost-Efficient Space-Time Adaptive Algorithm for Coupled Flow and Transport

TL;DR

This paper introduces a cost-efficient, space-time adaptive algorithm based on the Dual Weighted Residual method for coupled flow and transport problems, effectively handling convection dominance and varying dynamics.

Contribution

It develops a novel multirate, space-time slab approach with error indicators for coupled flow and transport, enhancing adaptivity and efficiency in complex simulations.

Findings

Algorithm performs well on benchmark problems.

Effective handling of convection-dominated transport.

Interaction of stabilization and adaptivity improves accuracy.

Abstract

In this work, a cost-efficient space-time adaptive algorithm based on the Dual Weighted Residual (DWR) method is developed and studied for a coupled model problem of flow and convection-dominated transport. Key ingredients are a multirate approach adapted to varying dynamics in time of the subproblems, weighted and non-weighted error indicators for the transport and flow problem, respectively, and the concept of space-time slabs based on tensor product spaces for the data structure. In numerical examples the performance of the underlying algorithm is studied for benchmark problems and applications of practical interest. Moreover, the interaction of stabilization and goal-oriented adaptivity is investigated for strongly convection-dominated transport.