arXiv subjects

Atakan Aygun

Publications and source records attributed to Atakan Aygun.

6 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↗

arXiv2024

Physics-Informed Neural Networks for Weakly Compressible Flows Using Galerkin-Boltzmann Formulation

In this work, we study the Galerkin-Boltzmann formulation within a physics-informed neural network (PINN) framework to solve flow problems in weakly compressible regimes. The Galerkin-Boltzmann equations are discretized with second-order Hermite polynomials in microscopic velocity space, which leads to a first-order conservation law with six equations. Reducing the output dimension makes this equation system particularly well suited for PINNs compared with the widely used D2Q9 lattice Boltzmann velocity space discretizations. We created two distinct neural networks to overcome the scale disparity between the equilibrium and non-equilibrium states in collision terms of the equations. We test the accuracy and performance of the formulation with benchmark problems and solutions for forward and inverse problems with limited data. Our findings show the potential of utilizing the Galerkin-Boltzmann formulation in PINN for weakly compressible flow problems.

physics.flu-dyn↗

arXiv2023

Physics-Informed Neural Networks for Mesh Deformation with Exact Boundary Enforcement

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information. We use linear elasticity equations for mesh deformation. To prevent vertex collisions or edge overlap, the mesh movement in this work is conducted in steps with relatively small movements. For moving boundary problems, the exact position of the boundary is essential for having an accurate solution. However, PINNs are frequently unable to satisfy Dirichlet boundary conditions exactly. To overcome this issue, we have used hard boundary condition enforcement to automatically satisfy Dirichlet boundary conditions. Specifically, we first trained a PINN with soft boundary conditions to obtain a particular solution. Then, this solution was tuned with exact boundary positions and a proper distance function by using a new PINN considering only the equation residual. To assess the accuracy of our approach, we used the classical translation and rotation tests and compared them with a proper mesh quality metric considering the change in the element area and shape. The results show the accuracy of this approach is comparable with that of finite element solutions. We also solved different moving boundary problems, resembling commonly used fluid-structure interaction problems. This work provides insight into using PINN for mesh-deformation problems without needing a discretization scheme with reasonable accuracy.

physics.flu-dyn↗

arXiv2022

Physics Informed Neural Networks for Two Dimensional Incompressible Thermal Convection Problems

Physics informed neural networks (PINNs) have drawn attention in recent years in engineering problems due to their effectiveness and ability to tackle the problems without generating complex meshes. PINNs use automatic differentiation to evaluate differential operators in conservation laws and hence do not need to have a discretization scheme. Using this ability, PINNs satisfy governing laws of physics in the loss function without any training data. In this work, we solve various incompressible thermal convection problems including real applications and problems with comparable numerical or analytical results. We first consider a channel problem with an analytical solution to show the accuracy of our network. Then, we solve a thermal convection problem in a closed enclosure in which the flow is only due to the temperature gradients on the boundaries. Lastly, we consider steady and unsteady partially blocked channel problems that resemble industrial applications to power electronics.

physics.flu-dyn↗