Work

Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators

Year: 2025

Type: preprint

Abstract: Overset grid methods handle complex geometries by overlapping simpler, geometry-fitted grids to cover the original, more complex domain. However, ensuring their stability---particularly at high orders---remains a theoretical challenge: although overset grid methods perform robustly in extensive practical use, general stability proofs are not available. In this work, we address this gap by developing a discrete counterpart to the recent well-posedness analysis of Kopriva, Gassner, and Nordström for continuous overset domain initial-boundary-value problems. To this end, we introduce the novel concept of sub-cell summation-by-parts (SBP) operators. These discrete derivative operators mimic integration by parts at a sub-cell level. By exploiting this sub-cell SBP property, we develop provably conservative and energy-stable overset grid methods for fixed one-dimensional overset domains that do not change with time or under grid refinement, providing a step toward stability proofs for overset grid methods based on the energy method.

Source: arXiv (Cornell University)

DOI: 10.1016/j.jcp.2026.115347

Authors: Glaubitz, Jan, Lampert, Joshua, Winters, Andrew R., Nordström, Jan

Institutions: Linköping University, Universität Hamburg, University of Johannesburg

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Vetenskapsrådet, University of Johannesburg

Awards: G3985256695, G5252384289, Neural Network Trained Schemes for Efficient Simulation of Complex Physics using Adaptive Mesh Refinement, Beyond polynomials: Summation-by-parts operators for general function spaces

OpenAlex ID: W7083844444

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