arXiv subjects

Süleyman Cengizci

Publications and source records attributed to Süleyman Cengizci.

3 recordsLinked to original sources

arXiv2026

A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder

This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov--Galerkin (SUPG) formulation is combined with the YZ$β$ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing---PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space--time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities.

physics.flu-dyn↗

arXiv2026

Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems

The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often generate spurious oscillations, requiring advanced stabilization techniques. However, even stabilized finite element methods may require additional regularization to accurately resolve localized steep layers. On the other hand, standalone physics-informed neural networks (PINNs) struggle to capture sharp solution structures in convection-dominated regimes and typically require a large number of training epochs. This work presents a hybrid computational framework that extends the PINN-Augmented SUPG with Shock-Capturing (PASSC) methodology from steady to unsteady problems. The approach combines a semi-discrete stabilized finite element method with a PINN-based correction strategy for transient convection-diffusion-reaction equations. Stabilization is achieved using the Streamline-Upwind Petrov-Galerkin (SUPG) formulation augmented with a YZbeta shock-capturing operator. Rather than training over the entire space-time domain, the neural network is applied selectively near the terminal time, enhancing the finite element solution using the last K_s temporal snapshots while enforcing residual constraints from the governing equations and boundary conditions. The network incorporates residual blocks with random Fourier features and employs progressive training with adaptive loss weighting. Numerical experiments on five benchmark problems, including boundary and interior layers, traveling waves, and nonlinear Burgers dynamics, demonstrate significant accuracy improvements at the terminal time compared to standalone stabilized finite element solutions.

math.NA↗

arXiv2019

A comparison between MMAE and SCEM for solving singularly perturbed linear boundary layer problems

In this study, we propose an efficient method so-called Successive Complementary Expansion Method (SCEM), that is based on generalized asymptotic expansions, for approximating to the solutions of singularly perturbed two-point boundary value problems. In this easy-applicable asymptotic method, in contrast to the well-known method the Method of Matched Asymptotic Expansions (MMAE), the matching process is not necessary to obtain uniformly valid approximations. The key point: A uniformly valid approximation is adopted first, and complementary functions are obtained imposing the corresponding boundary conditions. An illustrative and two numerical experiments are provided to show the implementation and numerical properties of the present method. Furthermore, MMAE results are also given in order to compare the numerical robustness of the methods. Numerical results and the comparisons demonstrate absolute superiority of SCEM over MMAE for linear problems.

math.NA↗