Development of discontinuous galerkin method 2 dimensional flow solver

Güngör, Osman
In this work, 2 dimensional flow solutions of Euler equations are presented from the developed discontinuous Galerkin method finite element method (DGFEM) solver on unstructured grids. Euler equations govern the inviscid and adiabatic flows with a set of hyperbolic equations. The discretization of governing equations for DGFEM is given in detail. The DGFEM discretization provides high order solutions on an element-compact stencil hence only elements having common boundary are coupled. The required elementwise operations and mathematical operations are revisited and derivations are provided when necessary. Among the two major approaches, modal and nodal, nodal DGFEM is employed. Gaussian quadrature is utilized in the evaluation of volume and surface integrals. The flux through the cell boundaries are calculated through flux functions and several flux functions are implemented and compared. Proper boundary conditions are employed on the solution space boundaries. Severaltestcasesinliteratureareusedforverificationandvalidationpurposes. The high order accuracy is easily achieved in problems with smooth solutions. On the other hand, problems with shocks requires stabilization techniques which may limit the order of accuracy or degrade solution success. The satisfactory results are obtained with comparison of experimental results which are carefully selected considering the fidelity of governing equations. Moreover, importance of curved wall boundary representations in high order methods are experienced. Furthermore, effect of grid adaptation around shocks or discontinues is pointed out.


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A numerical solution algorithm based on finite volume method is developed for unsteady, two-dimensional, depth-averaged shallow water flow equations. The model is verified using test cases from the literature and free surface data obtained from measurements in a laboratory flume. Experiments are carried out in a horizontal, rectangular channel with vertical solid boxes attached on the sidewalls to obtain freesurface data set in flows where three-dimensionality is significant. Experimental data contain both ...
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In this paper, a fundamental solution for the coupled convection-diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and ind...
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Citation Formats
O. Güngör, “Development of discontinuous galerkin method 2 dimensional flow solver,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Aerospace Engineering., Middle East Technical University, 2019.