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MHDRotor_M WINTER SCHOOL NUMHYP 2020:
Short Course on Advanced Numerical Methods for Hyperbolic Equations


Lecturers: Prof. Dr.-Ing. Michael Dumbser and Dr. Elena Gaburro
Dep. Civil and Environmental Engineering, Lab. Applied Mathematics, University of Trento, Italy.

Dates: From Monday 10th to Friday 14th of February 2020 (36 hours).
Timetable.

Venue: University of Trento, Via Mesiano, 77, I-38123 Trento, Italy.

SUMMARY

Shu-Osher The short course on advanced numerical methods consists of a structured intensive one-week programme of 36 hours of theoretical lectures and computer laboratory exercises on advanced numerical methods for hyperbolic partial differential equations with applications in engineering and science.

The course covers Finite Volume methods, the exact and approximate solution of the Riemann problem, second order TVD methods, higher order ENO, WENO and Discontinuous Galerkin methods, as well as the discretization of non-conservative problems.
Special emphasis is put also on numerical methods that are able to handle complex geometries.
In particular, unstructured Finite Volume and Discontinuous Galerkin schemes as well as mesh-free particle methods are presented.

The lectures on the theory will be supplemented with laboratory-based computer exercises to provide hands-on experience to all participants on the practical aspects of numerical methods for hyperbolic problems and applications using MATLAB programs specially designed for the course.

The course is primarily designed for PhD students and post-doctoral researchers in applied mathematics, engineering, physics, computer science and other scientific disciplines. The course may also be of interest to senior researchers in industry and research laboratories, as well as to senior academics.

COST

Students and post-docs: € 500
Senior academics and others: € 1000


The fees (free of “VAT tax” as art. 10 DPR 633/72) cover lectures, laboratory exercises, lecturing material and demonstration programs in MATLAB.
Furthermore, the course fee includes the coffee breaks and one social event (dinner).

REGISTRATION AND ADMINISTRATIVE INFORMATION

Participants must register via e-mail, sending the attached registration form (Word version or PDF version) to michael.dumbser@unitn.it.

Payment of the course fee must be made only after registration and after January 1st 2020, but before 1st February 2020 by bank transfer to the bank account you can find here attached.

Once registered for the course you can proceed and make the necessary arrangements for attending the course, such as travel arrangements, booking the hotel, etc. Once the payment has been made please send a copy of the receipt via e-mail to the address indicated above.

For further information on registration and payment, please e-mail to: Prof. Dr.-Ing. Michael Dumbser (michael.dumbser@unitn.it) or Dr. Elena Gaburro (elena.gaburro@unitn.it).

CONTENTS

TOVstar3D Review of basic theoretical aspects of hyperbolic conservation laws and numerical concepts for hyperbolic equations. Finite volume methods for one-dimensional systems. Godunov's method. The Riemann problem. Approximate Riemann solvers. Godunov-type finite volume methods for non-linear systems.

Construction of higher order non-oscillatory methods via non-linear schemes: TVD, ENO and WENO reconstruction procedures. Discontinuous Galerkin Finite Element methods for one-dimensional problems. The well-balanced property and numerical methods for non-conservative hyperbolic systems. Extension to multiple space dimensions on Cartesian grids.

Complex geometries using unstructured triangular meshes in two space dimensions and using mesh-free approaches. Mesh-based algorithms: Finite volume schemes on unstructured meshes for two-dimensional geometries. Second-order reconstruction and slope limiting on unstructured meshes. Applications to the shallow water equations and the Euler equations of compressible gas dynamics. High order discontinuous Galerkin finite element methods on unstructured meshes. Mesh-free algorithms: Introduction to Lagrangian particle methods. Guidelines for implementation of smooth particle hydrodynamics (SPH) based on approximate Riemann solvers.

On the last day, the course is rounded-off by advanced seminar-style lectures with outlooks to the following topics: better than second order schemes on unstructured meshes, high order methods on space-time adaptive grids (AMR), time-accurate local time stepping (LTS), high order Lagrangian schemes on moving unstructured meshes, applications to compressible multi-phase flows, electromagnetic and elastic wave propagation, nonlinear elasto-plasticity, numerical general relativity and the Einstein-Euler system.

ABOUT TRENTO AND THE DOLOMITES

The historical city of Trento is situated in the autonomous Italian region of Trentino - Südtirol, close to the world-famous mountains called Dolomites.

Trento is very easy to reach by car or train from Austria (150 km south of Innsbruck) and from Verona (90 km north of Verona).
The nearest and most convenient airport is Verona Airport, 15 minutes from the Verona train station.

The region around Trento is of extraordinary beauty, with its unique mountains and lakes that offer the participants many exciting outdoor activities like skiing, hiking or climbing.

You can find here some additional information about restaurants and public transportation in Trento.
Piazza Montagna Lago Picco

Past events

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09-13 September 2019: MultiMat 2019
Ninth International Conference on Numerical Methods for Multimaterial Fluid Flow
Hotel Villa Madruzzo, Trento, Italy

I'm a member of the local organizing committee: please feel free to contact me if you need any further information

Conference information:

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