arXiv subjects

Onur Ata

Publications and source records attributed to Onur Ata.

3 recordsLinked to original sources

arXiv2026

A High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for the Boltzmann Equation in Nearly Incompressible Flows

We propose the arbitrary Lagrangian-Eulerian (ALE) form of the Galerkin-Boltzmann formulation for the simulation of nearly incompressible flows with moving boundaries. The continuous Boltzmann equations are mapped to a reference state to compensate the mesh motion with an advection term. The resulting system is discretized in space using the discontinuous Galerkin method on unstructured meshes. A semi-analytic Runge-Kutta time discretization is used to overcome the stiffness introduced by the continuous Boltzmann equations. The well-known geometric conservation law is shown to be satisfied by the time and space discretizations and consistent update of geometric factors of the discretization. The implementation is on the GPU accelerated kernel library libParanumal and validated by a free stream preservation and moving Taylor-Green vortex test cases. Then, the capabilities are shown using a plunging symmetric airfoil in two-dimensions and moving carangiform fish in three-dimensions using perfectly matched layers.

physics.flu-dyn↗

arXiv2026

Hybrid ROM-PINN Framework for Closure Modeling in Convection-Dominated Systems

Reduced-order models (ROMs) have become an essential tool for reducing the computational cost of fluid flow simulations. While standard ROMs can efficiently approximate laminar flows, their accuracy often suffers in convection-dominated regimes due to the truncation of dynamically important modes. To account for the influence of unresolved scales, ROM closure models are commonly introduced. Classical closure strategies are typically based on phenomenological arguments or analogies with large eddy simulation (LES), often formulated within a variational multiscale (VMS) framework, in which the resolved and unresolved scales are explicitly separated and their interactions are systematically modeled. More recently, advances in data-driven modeling and machine learning have opened new opportunities to construct ROM closures that are both more accurate and more consistent with the underlying physics. In this work, we develop a new ROM closure that combines machine learning with physics-based modeling principles. The closure term is derived within a VMS framework, where the reduced solution space is decomposed into resolved and unresolved components. This VMS-derived closure term is then modeled using PhysicsInformed Neural Networks (PINNs) and incorporated into a newly constructed C-PINN-ROM. The resulting closure leverages high-fidelity data while enforcing physical constraints imposed by the reduced-order equations, thereby ensuring consistency with the underlying dynamics and enhanced robustness in convection-dominated regimes. Through this PINN-based framework, we demonstrate how physics-informed machine learning can substantially improve the accuracy and robustness of ROMs, effectively bridging classical multiscale closure modeling with state-of-the-art data-driven methodologies.

physics.flu-dyn↗

arXiv2026

Implicit Large Eddy Simulation of Nearly Incompressible Flows with a Discontinuous Galerkin-Boltzmann Formulation

We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann equations. The compactness and low-dissipative nature of the discontinuous Galerkin method are leveraged to mimic traditional large eddy simulations with subgrid-scale models. One of the key requirements of ILES is to provide dissipation only within a narrow band of high wavenumbers. This is validated through numerical experiments on the Taylor-Green Vortex problem in detail at a Reynolds number where varying scales of coherent turbulent structures are present. Furthermore, the approach is validated for external aerodynamic configurations by simulating the flow over a sphere at a Reynolds number of $Re=3700$, capturing the laminar-turbulent transition and the complex multiscale vortex dynamics characteristic of this regime. The results demonstrate the capability of the high-order DG-Boltzmann formulation to accurately capture transitional and turbulent flow features without the use of explicit sub-grid scale modeling, highlighting its potential as a robust and physically consistent framework for ILES of nearly incompressible turbulent flows.

physics.flu-dyn↗