Work

The Generalized Scalar Auxiliary Variable Applied to the Incompressible Boussinesq Equation

Year: 2026

Type: article

Abstract: This paper introduces a second-order time discretization for solving the incompressible Boussinesq equation. It uses the generalized scalar auxiliary variable (GSAV) and a backward differentiation formula (BDF), based on a Taylor expansion around $$t^{n+k}$$ t n + k for $$k\ge 3$$ k ≥ 3 . An exponential time integrator is used for the auxiliary variable to ensure stability independent of the time step size. We give rigorous asymptotic error estimates of the time-stepping scheme, thereby justifying its accuracy and stability. The scheme is reformulated into one amenable to a $$H^1$$ H 1 -conforming finite element discretization. Finally, we validate our theoretical results with numerical experiments using a Taylor–Hood-based finite element discretization and show its applicability to large-scale 3-dimensional problems.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03256-1

Authors: Andreas Wagner, Barbara Wohlmuth, Jan Zawallich

Institution: Technical University of Munich

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Bundesministerium für Bildung und Forschung