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 C Nguyen a J Peraire B Cockburn Department of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge MA 02139 USA School of Mathematics University of Minnesota Minneapolis MN 55455 USA article info Article history Received 21 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 Lesson Objective:. An equation is like a set of scales.. To keep it balanced, whatever you. do to one side you must do to the other.. Use this idea to solve equations like:. 3x + 1 = x + 7 . 2 (3x + 1) = 3 (x – 2). Multiplication . Equations. 3-3 Solving . Multiplication . Equations. Solve. Solution. GOAL. Find the value of the variable that makes the. equation TRUE.. The value that makes the equation true.. To isolate the variable (have the variable on one. 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 “ . Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. Mathematical Language. A . solution. of an equation is a number that make the equation true. 3x+2=17. To . solve. an equation means to find all its solution. Two equations are equivalent if they have the same solutions. 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 “ . Equations Using Algebra Tiles . Objectives. Solving Equations Involving the Distributive Property. Solving Multi-Step Equations. Solving Equations. The development of the equation solving model is based on two ideas.. 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