PPT-Discontinuous Galerkin Methods for Solving Euler Equations

Andrey Andreyev andreyevumdedu Adviser James Baeder baederumdedu Final Presentation May 7 2013 Motivation Computational Fluid Dynamics CFD is widely used in Engineering Design to obtain solutions to complex flow problems when testing is impossible or restrictively expensive CFD is also used in conjunction with testing to increase confidence in the design process. Arnold Franco Brezzi Bernardo Cockburn and Donatella Marini Department of Mathematics Penn State University University Park PA 16802 USA Dipartimento di Matematica and IANCNR Via Ferrata 1 27100 Pavia Italy School of Mathematics University of Min SA A shock capturing strategy for higher order Discontinuous Galerin approximations of scalar conservation laws is presented We show how the original explicit arti64257cial viscos ity methods proposed over 64257fty years ago for 64257nite volume meth SA Javier Bonet University of Wales Swansea Swansea SA2 8PP UK We describe a method for computing timedependent solutions to the compressible NavierStokes equations on variable geometries We introduce a continuous mapping between a 64257xed reference Brezzi 12 L D Marini 12 and E Suli Abstract In this paper we consider discontinuous Galerkin DG nite ele ment approximations of a model scalar linear hyperbolic equation We show that in order to ensure continuous stabilization of the method it suc calculus. for data. focm. : . budapest. : . july. : 2011. robert. . ghrist. andrea. . mitchell. university . professor of mathematics & . electrical/systems engineering. the university of . By Katherine Voorhees. Russell Sage College. April 6, 2013. A Theorem of Newton. Application and significance . A Theorem of Newton derives a relationship between the roots and the coefficients of a polynomial without regard to negative signs.. When an Euler path is impossible, we can get an approximate path. In the approximate path, some edges will need to be retraced. An . optimal approximation. of a Euler path is a path with the minimum number of edge . = number of vertices – number of edges + number of faces. Or in short-hand,. . . = |V| - |E| + |F|. where V = set of vertices. E = set of edges. F = set of faces. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Exploration. Is it possible to draw this figure without lifting your pencil from the paper and without tracing any of the lines more than once?. Leonard Euler. This problem is an 18. th. century problem that intrigued Swiss mathematician Leonard Euler (1707-1783).. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . mechanics. Irina Tezaur. 1. , . Maciej. Balajewicz. 2. 1. Extreme Scale Data Science & Analytics Department, Sandia National Laboratories. 2. Aerospace Engineering Department, University of Illinois Urbana-Champaign. Granville Sewell. Mathematics Dept.. University of Texas El Paso. PDE2D History. Work began 1974 in Caracas. , Venezuela. Sold as TWODEPEP by IMSL, 1980-1984. Sold as PDE/PROTRAN by IMSL, 1984-1991. “Analysis of a Finite Element Method: PDE/PROTRAN,” Springer . GCSE: Solving Quadratic Equations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd June 2015 Overview There are 4 ways in which we can solve quadratic equations.   1 By Factorising 2