A discontinuous Petrov-Galerkin finite-element framework for the simulation of microwave-heated flows
Abstract
We present a high-order multiphysics solver for the simulation of microwave-heated flows. The solver couples a discontinuous Petrov-Galerkin (DPG) finite element method for the time-harmonic Maxwell equations with continuous Galerkin finite element methods for the heat equation and the incompressible Navier-Stokes equations. We validate the electromagnetic solver against multiple benchmark problems: wave propagation in a rectangular waveguide, a cavity problem with a singular solution, and a microwave-heated obstacle problem, comparing our results against numerical and experimental data from the literature. The results confirm the validity of the implementation and demonstrate its ability to perform adaptive mesh refinement using the DPG method's built-in error estimator. The final part of the study showcases the capabilities of the multiphysics framework through simulations of microwave-heated flow around obstacles with singular geometric features. These results highlight the potential of the proposed framework for the simulation and optimization of microwave-assisted chemical processes. Finally, the developed high-order multiphysics solver has a low memory footprint, since the electromagnetic solver relies on a Conjugate Gradient (CG) iterative solver and the fluid solver is implemented in a matrix-free fashion, making the overall approach scalable and well-suited for large-scale parallel simulations.
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BibTeX
@misc{marquis2026discontinuous,
title = {{A discontinuous Petrov-Galerkin finite-element framework for the simulation of microwave-heated flows}},
author = {Oreste Marquis and Matthias Maier and Bruno Blais},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03155},
eprint = {2609.03155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03155},
}
RIS
TY - UNPB
TI - A discontinuous Petrov-Galerkin finite-element framework for the simulation of microwave-heated flows
AU - Oreste Marquis
AU - Matthias Maier
AU - Bruno Blais
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.03155
UR - https://arxiv.org/abs/2609.03155
AB - We present a high-order multiphysics solver for the simulation of microwave-heated flows. The solver couples a discontinuous Petrov-Galerkin (DPG) finite element method for the time-harmonic Maxwell equations with continuous Galerkin finite element methods for the heat equation and the incompressible Navier-Stokes equations. We validate the electromagnetic solver against multiple benchmark problems: wave propagation in a rectangular waveguide, a cavity problem with a singular solution, and a microwave-heated obstacle problem, comparing our results against numerical and experimental data from the literature. The results confirm the validity of the implementation and demonstrate its ability to perform adaptive mesh refinement using the DPG method's built-in error estimator. The final part of the study showcases the capabilities of the multiphysics framework through simulations of microwave-heated flow around obstacles with singular geometric features. These results highlight the potential of the proposed framework for the simulation and optimization of microwave-assisted chemical processes. Finally, the developed high-order multiphysics solver has a low memory footprint, since the electromagnetic solver relies on a Conjugate Gradient (CG) iterative solver and the fluid solver is implemented in a matrix-free fashion, making the overall approach scalable and well-suited for large-scale parallel simulations.
ER -