Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis (AMNA)

People Research Publications Teaching

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Part I Equations of Motion and Basic Ideas on Discretizations
1. The Design of Atmospheric Model Dynamical Cores
2. Waves, Hyperbolicity and Characteristics
3. Horizontal Discretizations
4. Vertical Discretizations
5. Time Discretization
6. Stabilizing Fast Waves

Part II Conservation Laws, Finite-Volume Methods, Remapping Techniques and Spherical Grids
7. Momentum, Vorticity and Transport: Considerations in the Design of a Finite-Volume Dynamical Core
8. Atmospheric Transport Schemes: Desirable Properties and a Semi-Lagrangian View on Finite-Volume Discretizations
9. Emerging Numerical Methods for Atmospheric Modeling
10. Voronoi Tessellations and Their Application to Climate and Global Modeling

Part III Practical Considerations for Dynamical Cores in Weather and Climate Models
11. Conservation in Dynamical Cores
12. Conservation of Mass and Energy for the Moist Atmospheric Primitive Equations on Unstructured Grids
13. Diffusion, Filters and Fixers in Atmospheric General Circulation Models
14. Kinetic Energy Spectra and Model Filters
15. The Dynamical Core in the Development of Weather and Climate Models
16. Refactoring Scientific Applications for Massive Parallelism

Audience:
Students from "Computer Simulation in Science", master students of applied and numerical mathematics but also students from atmospheric modeling.

Remarks:

Prerequisites:
Analysis I-II, Lineare Algebra I-II, Numerik gewöhnlicher und partieller Differentialgleichungen

Lecture Notes:

• R. Klein, S. Vater, E. Päschke, D. Ruprecht, Multiple Scales Methods in Meteorology, in: H. Steinrück (ed.), Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances, CISM Courses and Lectures 523, Springer, 2011, pp. 127-196.
• P.H. Lauritzen, C. Jablonowski, M.A. Taylor, R.D. Nair (Eds.), Numerical Techniques for Global Atmospheric Models, Lecture Notes in Computational Science and Engineering 80, Springer, 2011.

Literature:

• A.J. Chorin, J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer, 2000.
• D.R. Durran, Numerical Methods for Fluid Dynamics: With Applications to Geophysics, Texts in Applied Mathematics 32, Springer, 2nd ed. 2010.
• B. Gustafsson, Fundamentals of Scientific Computing, Texts in Computational Science and Engineering 8, Springer, 2011.
• M.H. Holmes, Introduction to Perturbation Methods, Springer, 1995.
• J. Kevorkian, J.D. Cole, Multiple Scale and Singular Perturbation Methods, Springer, Applied Mathematical Sciences 114, 1996.
• R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, 1990.
• A.J. Majda, Introduction to P.D.E.'s and Waves for the Atmosphere and Ocean, Courant Lecture Notes 9, American Mathematical Society & Courant Institute of Mathematical Sciences, 2002.
• W. Schneider, Mathematische Methoden der Strömungsmechanik, Vieweg, 1978.
• A. Staniforth, J. Thuburn, Horizontal grids for global weather and climate prediction models: a review, Quart. J. Royal Meteorolog. Soc. 138 (2012), 1-26.
• E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer, 3rd ed. 2009.
• Li Dong, Bin Wang, Trajectory-Tracking Scheme in Lagrangian Form for Solving Linear Advection Problems: Preliminary Tests, Mon. Weath. Rev. 140 (2012), 650-663.
• N. Hurl, W. Layton, Y. Li, C. Trenchea, Stability Analysis of the Crank-Nicolson-Leap-Frog method with the Robert-Asselin-Williams time filter, Preprint 2013.
• R.J. Smith, Minimizing time-stepping errors in numerical models of the atmosphere and ocean, Master's thesis, University of Reading (2010).
• J.G. Verwer, Convergence and component splitting for the Crank-Nicolson-Leap-Frog integration method Modelling, Analysis and Simulation (2009), 1-15.

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