Implementation of different flux evaluation schemes into a two-dimensional Euler solver

Download
2006
Eraslan, Elvan
This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe’s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruction methods. The flux splitting methods are applied to subsonic, transonic and supersonic flows over NACA0012 airfoil, as well as subsonic, transonic and supersonic flows in a channel. The comparison of the obtained results with each other and the ones in the literature is presented. The advantages and disadvantages of each scheme among others are identified.

Suggestions

Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids
Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007)
In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Solution of helmholtz type equations by differential quadrature method
Kuruş, Gülay; Tezer, Münevver; Department of Mathematics (2004)
This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
Inverse Sturm-Liouville Systems over the whole Real Line
Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010)
In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...
Citation Formats
E. Eraslan, “Implementation of different flux evaluation schemes into a two-dimensional Euler solver,” M.S. - Master of Science, Middle East Technical University, 2006.