Patch Bubbles for Advection-Dominated Steady and Unsteady Problems

Bänsch E, Morin P, Zocola I (2026)

Publication Type: Journal article

Publication year: 2026

Journal

International Journal For Numerical Methods in Fluids Wiley-Blackwell

DOI: 10.1002/fld.70077

Abstract

A novel variant of the residual-free bubble method (RFB) for advection-dominated problems is presented. Since the usual RFB still suffers from oscillations and strong under/overshoots, the bubble space is enriched by patch bubbles, giving more freedom to the bubble space. We use a recursive and efficient approach to accurately compute the bubbles. Numerical experiments clearly demonstrate the superiority of our method compared to the standard RFB. While similar in spirit to the enhanced residual-free bubble (eRFB) method by Cangiani and Süli [7, 8], our approach differs in the definition and computation of the additional bubbles. In addition, we extend the methodology to solve problems with non constant coefficients and we develop a novel bubble-based stabilization technique for time-dependent problems, which performs very accurately.

Authors with CRIS profile

Eberhard Bänsch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

National University of the Littoral / Universidad Nacional del Litoral (UNL) AR Argentina (AR)

How to cite

APA:

Bänsch, E., Morin, P., & Zocola, I. (2026). Patch Bubbles for Advection-Dominated Steady and Unsteady Problems. International Journal For Numerical Methods in Fluids. https://doi.org/10.1002/fld.70077

MLA:

Bänsch, Eberhard, Pedro Morin, and Itatí Zocola. "Patch Bubbles for Advection-Dominated Steady and Unsteady Problems." International Journal For Numerical Methods in Fluids (2026).

BibTeX: Download