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 * ''Finite Difference Method for boundary value problems''
   * [attachment:Summary2.html Summary 2]
   * Recommended literature: [1], Additional resources: [5] 		## * ''Finite Difference Method for boundary value problems''
## * [attachment:Summary2.html Summary 2]
## * Recommended literature: [1], Additional resources: [5]
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 * ''Stability of Finite Difference schemes''
   * [attachment:stability.pdf Summary 3]
   * Additional resources: [7, 8, 9, 10] 		## * ''Stability of Finite Difference schemes''
## * [attachment:stability.pdf Summary 3]
## * Additional resources: [7, 8, 9, 10]
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 * ''Explicit schemes for spatio-temporal discretization''
   * [attachment:RK.pdf Runge-Kutta method]
   * [attachment:guidlines5.pdf Periodic boundary conditions for explicit schemes] 		## * ''Explicit schemes for spatio-temporal discretization''
## * [attachment:RK.pdf Runge-Kutta method]
## * [attachment:guidlines5.pdf Periodic boundary conditions for explicit schemes]
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 * ''Implicit schemes for spatio-temporal discretization''
   * [attachment:guidelines6.pdf Boundary conditions for implicit schemes] 		## * ''Implicit schemes for spatio-temporal discretization''
## * [attachment:guidelines6.pdf Boundary conditions for implicit schemes]
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 * ''2D time-dependent problems and systems of PDEs '' ## * ''2D time-dependent problems and systems of PDEs ''
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 * ''Non-linear problems''
   * [attachment:nonlinear.pdf Numerical methods for non-linear problems]
   * [attachment:SolvedExample6.html Solved illustrative example] 		## * ''Non-linear problems''
## * [attachment:nonlinear.pdf Numerical methods for non-linear problems]
## * [attachment:SolvedExample6.html Solved illustrative example]
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 * ''Bonus examples'' ## * ''Bonus examples''
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 * ''Questions and Answers'' ## * ''Questions and Answers''
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== Team Project == ##== Team Project ==
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 || The assignment of the team project will be released around the middle of the semester. ||
 || This assignment has to be done by groups of two or three (too long otherwise !). ||
 || Some template codes are provided, they have to be filled in and submitted together with the final report.|| 		## || The assignment of the team project will be released around the middle of the semester. ||
## || This assignment has to be done by groups of two or three (too long otherwise !). ||
## || Some template codes are provided, they have to be filled in and submitted together with the final report.||
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== Recommended literature ==
[1] Lecture notes for the course [https://tiss.tuwien.ac.at/course/courseDetails.xhtml?courseNr=302017 LVA-Nr. 302.017]: Grundlagen der numerischen Methoden der Stömungs- und Wärmetechnik, TU Wien 		##== Recommended literature ==
##[1] Lecture notes for the course [https://tiss.tuwien.ac.at/course/courseDetails.xhtml?courseNr=302017 LVA-Nr. 302.017]: Grundlagen der numerischen Methoden der Stömungs- und Wärmetechnik, TU Wien
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[3] [https://www.springer.com/de/book/9783540530589 Fletcher, C. (1998), 'Partial Differential Equations' In Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques, Springer, Berlin.] ##[3] [https://www.springer.com/de/book/9783540530589 Fletcher, C. (1998), 'Partial Differential Equations' In Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques, Springer, Berlin.]
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[4] [https://www.springer.com/de/book/9783540678533 Wesseling, P. (2001), 'Classification of partial differential equations' In Principles of Computational Fluid Dynamics, Vol. 29 of Springer Series in Computational Mathematics, Springer, Berlin.] ##[4] [https://www.springer.com/de/book/9783540678533 Wesseling, P. (2001), 'Classification of partial differential equations' In Principles of Computational Fluid Dynamics, Vol. 29 of Springer Series in Computational Mathematics, Springer, Berlin.]
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[11] Wilhelm Schneider, Mathematische Methoden der Strömungsmechanik, 1. Auflage Braunschweig, Vieweg 1978, ISBN 3-528-03574-0 ##[11] Wilhelm Schneider, Mathematische Methoden der Strömungsmechanik, 1. Auflage Braunschweig, Vieweg 1978, ISBN 3-528-03574-0
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== Additional resources == ##== Additional resources ==
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[2] [http://how.gi.alaska.edu/ao/sim/chapters/chap3.pdf Otto, A. (2011), 'Classification of PDE's and Related Properties' In Methods of Numerical Simulation in Fluids and Plasmas. Lecture notes, University of Alaska] ##[2] [http://how.gi.alaska.edu/ao/sim/chapters/chap3.pdf Otto, A. (2011), 'Classification of PDE's and Related Properties' In Methods of Numerical Simulation in Fluids and Plasmas. Lecture notes, University of Alaska]
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[5] [http://cfdblogvienna.blogspot.com/ 'CFD Education Center - Vienna', URL: http://cfdblogvienna.blogspot.com/] ##[5] [http://cfdblogvienna.blogspot.com/ 'CFD Education Center - Vienna', URL: http://cfdblogvienna.blogspot.com/]
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[6] [https://web.stanford.edu/class/math220a/lecturenotes.html Levandosky, J. (2002), 'Partial Differential Equations of Applied Mathematics', Course Math 220A, Lecture notes, Stanford University] ##[6] [https://web.stanford.edu/class/math220a/lecturenotes.html Levandosky, J. (2002), 'Partial Differential Equations of Applied Mathematics', Course Math 220A, Lecture notes, Stanford University]
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[7] [https://ocw.mit.edu/courses/mathematics/18-336-numerical-methods-for-partial-differential-equations-spring-2009/lecture-notes/ Seibold, B. (2009), 'Numerical Methods for Partial Differential Equations', Course No. 18.336, Lecture notes, MIT]. Shared under [http://creativecommons.org/licenses/by-nc-sa/4.0/legalcode this license]. ##[7] [https://ocw.mit.edu/courses/mathematics/18-336-numerical-methods-for-partial-differential-equations-spring-2009/lecture-notes/ Seibold, B. (2009), 'Numerical Methods for Partial Differential Equations', Course No. 18.336, Lecture notes, MIT]. Shared under [http://creativecommons.org/licenses/by-nc-sa/4.0/legalcode this license].
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[8] [https://akmitra.public.iastate.edu/aero361/design_web/Laplace.pdf Mitra, A. K., 'Finite Difference Method for the Solution of Laplace Equation', Lecture notes, Iowa State University] ##[8] [https://akmitra.public.iastate.edu/aero361/design_web/Laplace.pdf Mitra, A. K., 'Finite Difference Method for the Solution of Laplace Equation', Lecture notes, Iowa State University]
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[9] [https://www.12000.org/my_notes/mma_matlab_control/KERNEL/KEse83.htm Abbasi, N. M. (2019) 'Chapter 2.44: Generate sparse matrix for the Laplacian differential operator for 3D grid' In 'How to solve basic engineering and mathematics problems using Mathematica, Matlab and Maple', Blog post] ##[9] [https://www.12000.org/my_notes/mma_matlab_control/KERNEL/KEse83.htm Abbasi, N. M. (2019) 'Chapter 2.44: Generate sparse matrix for the Laplacian differential operator for 3D grid' In 'How to solve basic engineering and mathematics problems using Mathematica, Matlab and Maple', Blog post]
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[10] [http://www.public.asu.edu/~hhuang38/mae384_2009_pde_note3.pdf Huang, H.-P. (2012), 'Introduction to Partial Differential Equation - III. Numerical methods' In 'Numerical Methods for Engineers', Course MAE384, Lecture notes, Arizona State University] ##[10] [http://www.public.asu.edu/~hhuang38/mae384_2009_pde_note3.pdf Huang, H.-P. (2012), 'Introduction to Partial Differential Equation - III. Numerical methods' In 'Numerical Methods for Engineers', Course MAE384, Lecture notes, Arizona State University]
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##Lösungen von Programmieraufgaben sind als Programme per Email abzugeben. ####Lösungen von Programmieraufgaben sind als Programme per Email abzugeben.

UE Fundamentals of Numerical Thermo-Fluid Dynamics, 322.061

This course in TISS