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Computational Mathematics


Computational Mathematics

Logo UHasselt Universiteit Hasselt - Knowledge in action

ALEXANDER JAUST

Alexander Jaust, M.Sc.

Room nr.: D250A
E-mail: alexander.jaust@uhasselt.be

Address: 
Campus Diepenbeek
Agoralaan Gebouw D
BE 3590 Diepenbeek
Belgium

I'm also affiliated with:

MathCCES
Department of Mathematics
RWTH Aachen University
Schinkelstr. 2
D-52062 Aachen
Germany

You can find my homepage at RWTH Aachen University here.


  • High-Order Methods for Convection-Dominated Problems
  • Hybridized DG methods
  • High-Performance Computing

My publications while at UHasselt can also be found here.

Journal Publications

  • A. Jaust, B. Reuter, V. Aizinger, J. Schütz and P. Knabner, FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation, submitted
  • J. Schütz, D.C. Seal and A. Jaust, Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations, Journal of Scientific Computing, 2017, doi:10.1007/s10915-017-0485-9
  • A. Jaust, J. Schütz, D.C. Seal: Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws, Journal of Scientific Computing, Volume 69, Issue 2, pp 866–891, doi:10.1007/s10915-016-0221-x
  • A. Jaust, J. Schütz: A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows, Computers & Fluids, Volume 98, 2 July 2014, Pages 177-185, ISSN 0045-7930, doi:10.1016/j.compfluid.2014.01.019

Proceedings

  • A. Jaust, J. Schütz: General linear methods for time-dependent PDEs, accepted
  • A. Jaust, J. Schütz, V. Aizinger: An efficient linear solver for the hybridized discontinuous Galerkin method, Proceedings in Applied Mathematics and Mechanics, 845-846, 2016, doi:10.1002/pamm.201610411
  • A. Jaust, J. Schütz, D.C. Seal : Multiderivative time-integrators for the hybridized discontinuous Galerkin method, Conference Proceedings of the YIC GACM 2015, 2015, urn:nbn:de:hbz:82-rwth-2015-039806
  • A. Jaust, B. Morcinkowski, S. Pischinger and J. Ewald: Modeling of Transport and Mixing Phenomena in Turbulent Flows in Closed Domains, SAE Technical Paper 2015-01-0399, 2015, doi:10.4271/2015-01-0399
  • A. Jaust, J. Schütz, M. Woopen: An HDG Method for unsteady compressible flows, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Lecture Notes in Computational Science and Engineering, Vol 106, 2015, Pages 267-274, ISSN 1439-7358, doi:10.1007/978-3-319-19800-2
  • A. Jaust, J. Schütz, M. Woopen: A Hybridized Discontinuous Galerkin Method for Unsteady Flows with Shock-Capturing, AIAA Paper 2014-2781, American Institute of Aeronautics and Astronautics, 2014, doi:10.2514/6.2014-2781

Miscellaneous

  • A Hybridized Discontinuous Galerkin Method for Time-Dependent Compressible Flows, Master's thesis, RWTH Aachen University, Germany, 2013 [PDF]
  • Entwicklung eines Mehrzonenmischungsmodells für die numerische Simulation eines CAI Motors (engl. title: Development of a multi-zone mixing model for the numerical simulation of a CAI engine), Bachelor's thesis, RWTH Aachen University, 2011
  • Implizite Zeitintegrationsverfahren gekoppelt mit WENO Verfahren hoher Ordnung zur Lösung von kompressiblen Erhaltungsgleichungen der Strömungsmechanik (engl. title: Implicit time integration coupled to high-order WENO schemes for compressible flow problems, Project thesis, RWTH Aachen University, Germany, 2011

Talks

  • Multiderivative time integrators for a hybridized discontinuous Galerkin method, ACOMEN 2017, Ghent, Belgium, 2017
  • A hybridized DG method for unsteady flow problems, VSC Users day, Brussels, Belgium, 2017 (1 minute short talk)
  • A hybridized discontinuous Galerkin method for unsteady flow problems, CMAT seminar, Diepenbeek, Belgium, 2017
  • Multiderivative time-integrators for the hybridized discontinuous Galerkin method, IGPM seminar on current topics in numerics, Amsterdam, The Netherlands, 2016
  • Discontinuous Galerkin methods, Seminar Series on Hot Topics in Applied Mathematics by SIAM student chapter Aachen, Aachen, Germany, 2016
  • An evaluation of shock-capturing schemes for hybridized discontinuous Galerkin methods, XVI International Conference on Hyperbolic Problems Theory, Numerics, Applications (Hyp2016), Aachen, Germany, 2016
  • An efficient linear solver for the hybridized discontinuous Galerkin method, Joint annual meeting of DMV and GAMM, Braunschweig, Germany, 2016
  • Efficient time integration for the HDG method, DMV Jahrestagung, Hamburg, Germany, 2015 (as replacement for J. Schütz)
  • Multiderivative time-integrators for the hybridized discontinuous Galerkin method, YIC GACM 2015, Aachen, Germany, 2015
  • Multiderivative time integrators for a hybridized discontinuous Galerkin method, MathCCES lunch seminar, Aachen, Germany 2015
  • A hybridized DG method for unsteady compressible flows, IGPM seminar on current topics in numerics, Leer, Germany, 2014
  • An HDG method for unsteady compressible flows, International Conference on Spectral and High Order Methods, Salt Lake City, USA, 2014
  • A hybridized discontinuous Galerkin method for unsteady flows with shock-capturing, AIAA Aviation, Atlanta, USA, 2014
  • A hybridized discontinuous Galerkin method for time-dependent compressible flows, MathCCES lunch seminar, Aachen, Germany 2014

Posters

  • A hybridized discontinuous Galerkin method for unsteady flow problems -  A versatile method for a wide range of problems in fluid dynamics?, Summer School: Upscaling techniques for mathematical models involving multiple scales, Hasselt Belgium, 2017 (Awarded special poster award)
  • A hybridized DG method for unsteady flow problems - Towards an efficient method for a wide range of flow problems, Netgen User Meeting, Vienna, Austria, 2017
  • A hybridized DG method for unsteady flow problems - An efficient method for a huge range of flows, VSC Users day, Brussels, Belgium, 2017

I am working on the extension of a hybridized discontinuous Galerkin method for unsteady flow problems. It is a so-called high-order method, i.e. the error decreases with third order or more under uniform mesh refinement.

Euler equations

Flows at high Mach numbers , i.e. supersonic flows, can be modeled by the Euler equations. These neglect viscous effects of a fluid as these only have a small influence on the resulting flow. However, in many applications these flows shocks develop. In this case we apply an artificial viscosity model for stabilizing the scheme.

Close-up of the shock interactions of a double Mach wedge.

Navier-Stokes equations

For modeling viscous flow we use the compressible Navier-Stokes equations. These flows develop boundary layers when the fluid passes rigid walls since no-slip condition conditions are enforced on these surfaces.

A `classical' phenomenon for viscous flows is the Karman vortex street. If a viscous fluid flows around an obstacle at moderate Reynolds numbers vortices shed periodically. It has been intensively studied by many scientists. Therefore, it is often used for verification of numerial methods. The actual behavior of the flow depends on the Reynolds number and the shape of the obstacle.

You can also let the fluid flow around obstacles such as the CMAT writing (see also top left of the homepage):

Flow around CMAT logo

More images will follow soon! 

References

Please look in our papers and especially the references therein.