An adaptive non-symmetric finite volume and boundary element coupling method for a fluid mechanics interface problem

TL;DR

This paper introduces an adaptive non-symmetric finite volume and boundary element coupling method for interface problems in fluid mechanics, featuring a robust residual error estimator and effective adaptive mesh refinement.

Contribution

It presents a novel adaptive coupling approach combining FVM and BEM with a residual error estimator for interface problems, improving robustness and efficiency.

Findings

Error estimator is robust against data variation.

Adaptive mesh refinement improves solution accuracy.

Method effectively solves fluid mechanics interface problems.

Abstract

We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the complement, an unbounded domain. Based on the non-symmetric coupling of the finite volume method and boundary element method of [Erath et al., arXiv:1509.00440, 2015] we introduce a robust residual error estimator. The upper bound of the error in an energy (semi)norm is robust against variation of the model data. The lower bound, however, additionally depends on the Peclet number. In several examples we use the local contributions of the a~posteriori error estimator to steer an adaptive mesh-refining algorithm. The adaptive FVM-BEM coupling turns out to be an efficient method especially to solve problems from fluid mechanics, mainly because of the local flux conservation and the stable approximation of convection dominated problems.