arXiv subjects

Ceren Gürkan

Publications and source records attributed to Ceren Gürkan.

5 recordsLinked to original sources

arXiv2023

An Automated and Efficient Aerodynamic Design and Analysis Framework Integrated to PANAIR

Aircraft design is an iterative process that requires an estimation of aerodynamic characteristics including drag and lift coefficients, stall behavior, velocity, and pressure profiles repeatedly, especially in the conceptual design phase. PanAir is a high-order aerodynamic panel method-based algorithm developed as a part of the Public Domain Aeronautical Software program mostly with NASA sponsorship. It is based upon potential flow theory and is used to numerically compute lift, induced drag, and moment coefficients of the aircraft in both subsonic and supersonic flight regimes. Quoting from developers it is the most versatile and accurate of all the linear theory panel codes. PanAir is a classical software that requires geometric data as an input in the form of a PanAir-compatible format; however, commonly used Computer-Aided Design Software packages no longer conform to the PanAir input format. Likewise, PanAir produces its output in a PanAir-specific output file which is not compatible with commonly used visualization software. The input geometry required by PanAir and its output, therefore, involves significant manual preand post-processing using intermediary software. The work proposed here is an automated pre and post-processor to be used together with PanAir. With the environment proposed in this work, manipulation of input and output data using several intermediary software to and from PanAir is bypassed successfully. The proposed environment is validated over a Cessna 210 aircraft geometry with a modified NLF (1)-0414 airfoil. The aircraft is numerically analyzed using PanAir together

cs.CE↗

arXiv2023

eXtended Hybridizable Discontinous Galerkin (X-HDG) Method for Linear Convection-Diffusion Equations on Unfitted Domains

In this work, we propose a novel strategy for the numerical solution of linear convection diffusion equation (CDE) over unfitted domains. In the proposed numerical scheme, strategies from high order Hybridized Discontinuous Galerkin method and eXtended Finite Element method is combined with the level set definition of the boundaries. The proposed scheme and hence, is named as eXtended Hybridizable Discontinuous Galerkin (XHDG) method. In this regard, the Hybridizable Discontinuous Galerkin (HDG) method is eXtended to the unfitted domains; i.e, the computational mesh does not need to fit to the domain boundary; instead, the boundary is defined by a level set function and cuts through the background mesh arbitrarily. The original unknown structure of HDG and its hybrid nature ensuring the local conservation of fluxes is kept, while developing a modified bilinear form for the elements cut by the boundary. At every cut element, an auxiliary nodal trace variable on the boundary is introduced, which is eliminated afterwards while imposing the boundary conditions. Both stationary and time dependent CDEs are studied over a range of flow regimes from diffusion to convection dominated; using high order $(p \leq 4)$ XHDG through benchmark numerical examples over arbitrary unfitted domains. Results proved that XHDG inherits optimal $(p + 1)$ and super $(p + 2)$ convergence properties of HDG while removing the fitting mesh restriction.

math.NA↗

arXiv2020

A Comparison Between Meshless Radial Basis Function Collocation Method and Finite Element Method for Solving Poisson and Stokes Problems

Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several criteria. The accuracy of Radial Basis Function Collocation Method with multiquadrics is enhanced by implementing a shape parameter optimization algorithm. For the time-dependent problems, time discretization is conducted using Backward Euler Method. The performances are assessed over the accuracy, runtime, condition number, and ease of implementation criteria. Three kinds of errors were calculated; least square error, root mean square error and maximum relative error. To calculate the least square error while using meshless Radial Basis Function Collocation Method, a novel technique is implemented. Imaginary numerical solution surfaces are created and then the volume between those imaginary surfaces and the analytic solution surfaces is calculated, enabling a fair error calculation. Lastly, all solutions are put together and solution trends are observed over the number of solution nodes vs. runtime, accuracy vs. runtime, and accuracy vs. the number of nodes. The assessment indicates the criteria under which Finite Element Method perform better and those when Radial Basis Function Collocation Method outperforms its mesh dependent counterpart.

math.NA↗

arXiv2020

Stabilized CutDG methods for advection-reaction problems

We develop novel stabilized cut discontinuous Galerkin (CutDG) methods for advection-reaction problems. The domain of interest is embedded into a structured, unfitted background mesh in $\mathbb{R}^d$ where the domain boundary can cut through the mesh in an arbitrary fashion. To cope with robustness problems caused by small cut elements, we introduce ghost penalties in the vicinity of the embedded boundary to stabilize certain (semi)-norms associated with the advection and reaction operator. A few abstract assumptions on the ghost penalties are identified enabling us to derive geometrically robust and optimal a priori error and condition number estimates for the stationary advection-reaction problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. The theoretical results are corroborated by a number of computational studies for various approximation orders and for two and three-dimensional test problems.

math.NA↗

arXiv2018

A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems

We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of el- liptic boundary value and interface problems on complicated domains. The domain of interest is embedded in a structured, unfitted background mesh in R d , so that the boundary or interface can cut through it in an arbitrary fashion. The method is based on an unfitted variant of the classical symmetric interior penalty method using piecewise discontinuous polynomials defined on the back- ground mesh. Instead of the cell agglomeration technique commonly used in previously introduced unfitted discontinuous Galerkin methods, we employ and extend ghost penalty techniques from recently developed continuous cut finite element methods, which allows for a minimal extension of existing fitted discontinuous Galerkin software to handle unfitted geometries. Identifying four abstract assumptions on the ghost penalty, we derive geometrically robust a priori error and con- dition number estimates for the Poisson boundary value problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. We also demonstrate how the framework can be elegantly applied to discretize high contrast interface problems. The theoretical results are illustrated by a number of numerical experiments for various approximation orders and for two and three-dimensional test problems.

math.NA↗