Department of Natural and Environmental Sciences
Group Photo: Numerical Simulation Research Group

Numerical Simulation Club

Michael Urs Lars Kastor, Tristan Probst, Anne Von Nida, Prof. Dr. Anna Hundertmark, Dr. Stephan Schmitz

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Numerische Simulation

Rheinland-Pfälzische 
Technische Universität
Kaiserslautern-Landau (RPTU)

Fortstraße 7 76829 Landau

Building I, 1. OG

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In the workgroup Numerical Simulation, change processes from a wide variety of fields of life such as mathematics, physics, meteorology, hydrology and medical technology are modeled and simulated.

The basic models of such change processes are always ordinary or partial differential equations. The analysis of the corresponding mathematical model (e.g. correct problem definition, existence of solutions), the finding of suitable approximations of the solutions by numerical discretization methods and the stability of these approximation methods are central points.

Research projects of the AG Numerical Simulation

Projects overview

  • MSO: "Modeling, Simulation, Optimization", Research Initiative of the Federal State of Rhineland-Palatinate, Potential Department of Mathematics, PRTU Kaiserslautern-Landau
  • CZS project AI-Care: "Artificial Intelligence for treating Cancer therapy Resistance".
  • Project GEL: "Supersonic Flow Simulations and Impactation Processes"

Project overview

  • BMBF joint project MLgSA: "Data- and simulation-based exploration, analysis and treatment of vasoconstrictions for the prevention of ischemic strokes."
  • FSI-COMPLEX FLUIDS project (HU 1885/1-2, ZA 613/1-1): "Mathematical modeling and numerical simulation of fluid-structure interaction for complex viscous fluids"

Publications

  • Parameter conditioned interpretable U-Net surrogate model for data-driven predictions of convection-diffusion-reaction processes, M. U. L. Kastor, J. Rottmayer, A. Hundertmark, N. R. Gauger, preprint 2026, http://arxiv.org/abs/2601.22654
  • Resistance outlet boundary condition in the FSI-modelling of compliant carotid artery tree with generalized
    linear-elastic model, T. Probst, A. Shiravand, G. Cattaneo, A. Hundertmark, preprint 2025.
  • Design study of a rocket-borne free-flow aerosol collector for supersonic speed deployment by means of numerical efficiency analyses, B. Klug, R. Weigel, K. Kandler, M. Baumgartner, A. Hundertmark, T. Böttger, K. D. Wilhelm, H. Rott, T. Kenntner, preprint 2024. public peer review: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-510/

  • Simulation of Compliance in a Humanoid Carotid Artery with Resistance Boundary Conditions, K. Richter, T. Probst, A. Hundertmark, Proceedings Topical Problems of Fluid Mechanics 2025, Prague, 2025, pp. 201, https://doi.org/10.14311/TPFM.2025.027
  • Fabrication, characterization and numerical validation of a novel thin-wall hydrogel vessel model for cardiovascular research based on a patient-specific stenotic carotid artery bifurcation, Shiravand, A., Richter, K., Willmann, P., Eulzer P., Lawonn K., Hundertmark A., Cattaneo G., Sci Rep14, 16301 (2024). https://doi.org/10.1038/s41598-024-66777-5
  • Instantaneous Visual Analysis of Blood Flow in StenosesUsing Morphological Similarity, P. Eulzer, K. Richter, A. Hundertmark, R. Wickenhöfer, C. M. Klingner, K. Lawonn, Computer Graphics forum Vol 43 (2024), No 3, http://dx.doi.org/10.1111/cgf.15081.
  • COMSOL ® simulations of supersonic flow fields to study trajectories of aerosols and their impact efficiency on a rocket- borne particle collector, Klug B. S., Hundertmark A., Weigel R., Comsol Conference 2023 Munich, 2023, ISBN 978-1-7364524-1-7, download pdf.
  • Utilizing COMSOL® in a workflow to assess stroke risks in a large set of patients carotid arteries, Probst T., Richter K., Hundertmark, A., Comsol Conference 2023 Munich, 2023, ISBN 978-1-7364524-1-7, download pdf.
  • Visualizing Carotid Stenoses for Stroke Treatment and PreventionP. Eulzer, K. Richter, A. Hundertmark, M. Meuschke, R. Wickenhöfer, C. M. Klingner, K. Lawonn, EUROVIS 2023/ T. W. Kuhlen and R. G. Raidou(Dirk Bartz Prize).
  • Longitudinal wall shear stress evaluation using centerline projection approach in the numerical simulations of the patient-based carotid artery, T. Probst, K. Richter, A. Hundertmark, P. Eulzer, K. Lawonn), Comput Methods Biomech Biomed Engin. 2024 Mar; 27(3):347-364, DOI: 10.1080/10255842.2023.2185478, arXiv:2204.04018
  • Automatic Cutting and Flattening of Carotid Artery Geometries, P. Eulzer, K. Richter, M. Meuschke, A. Hundertmark, and K. Lawonn, in Proceedings of Eurographics Workshop on Visual Computing for Biology and Medicine 2021, (Editors: S. Oeltze-Jafra, N. N. Smit, and B. Sommer), diglib
  • The effect of turbulence on the accretional growth of graupel, Jost A, Szakall M., Diehl K., Mitra S. K., A. Hundertmark, Klug B. S., Borrmann S., Journal of the Athmospheric Sciences, 2019, published online doi.org/10.1175/JAS-D-18-0200.1
  • Luka Grubisic, Vadim Kostrykin, Konstantin A. Makarov, Kresimir Veselic, Stephan Schmitz,The Tan 2Theta Theorem in Fluid Dynamics, J. Spectr. Theory 9 (2019), no.4, 1431-1457 (online first DOI 10.4171/JST/282)[arXiv 1708.00509].
  • On the convergence of the fixed point iterations for geometry in a fluid-structure interaction problem, A. Hundertmark, Journal of Differential Equations, Vol. 267, Issue 12, 2019, p. 7002-70462, published online doi.org/10.1016/j.jde.2019.07.009
  • A rescaling algorithm for the numerical solution to the porous media equation in a two-component domain, J. Filo, A. Hundertmark-Zaušková, accepted in Communications in Nonlinear Science and Numerical Simulation, published online 31 of March 2016, doi:10.1016/j.cnsns.2016.03.011
  • Numerical simulation of glottal flow in surgically altered larynx, A. Hundertmark-Zaušková, R. Lehmann, M.Hess, F. Müller), Proceedings in Applied Mathematics and Mechanics 2016, Ed. Gesellschaft für Angewandte Mathematik und Mechanik, Vol. 16, Issue 1, p. 843-844, DOI: 10.1002/pamm.201610410
  • On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear dependent fluid, A. Hundermark-Zaušková, M. Lukacova, S. Necasova), Journal of the Mathematical Society of Japan, Vol. 68, No 1, January 2016, 193-243, (accepted 2014), doi:10.2969/jmsj/06810193
  • Konstantin A. Makarov, Stephan Schmitz, Albrecht Seelmann, On invariant graph subspaces, Integr. Equ. Oper. Theory 85 (2016), 399 - 425[arXiv 1509.07984].
  • Stephan Schmitz, Representation theorems for indefinite quadratic forms without spectral gap, Integr. Equ. Oper. Theory 83 (2015), 73-94[arXiv 1409.2409].
  • Kinematic splitting algorithm for fluid-structure interaction in hemodynamics, M. Lukacova, G. Rusnakova, A. Hundertmark-Zaušková,Computer Methods in Applied Mechanics and Engineering 265, 2013, 83-106, sciencedirect
  • Numerical simulation of glottal flow, A. Hundertmark-Zaušková, R. Lehmann, M. Hess, F. Mueller), Computers in Biology and Medicine 43/12, 2013, 2177-2185, sciencedirect
  • Numerical study of shear-dependent non-Newtonian fluids in compliant vessels, A. Hundertmark-Zaušková, M. Lukacova, Computers and Mathematics with Applications 60, 2010, 572-590 sciencedirect
  • Large time step finite volume evolution Galerkin methods, A. Hundertmark-Zaušková, M. Lukacova, F. Prill , Journal of Scientific Computing, Volume 48 Issue 1-3, 2011, pp 227-240, springerlink, published online 2010, DOI:10.1007/s10915-010-9443-5
  • 2D Navier-Stokes Equations in a Time Dependent Domain with Neumann Type Boundary Conditions, J. Filo, A. Zaušková, Journal of Mathematical Fluid Mechanics 10, 2010, 1 - 46 springerlink, published online 2008,
  • Numerical modeling of shear-thinning non-Newtonian flows in compliant vessels, Anna Zaušková and Mária Lukáčová-Medvid'ová, PAMM 2007, Vol 7, doi.org/10.1002/pamm.200700059
  • Mathematical Modeling and Numerical Simulation of Blood Flow in Compliant Vessels, M. Lukáčová-Medviďová, Anna Zaušková, Proceedings of ECCOMAS 2008, Venice 2008
  • Numerical Modeling of Shear-Thinning non-Newtonian Flow in Compliant Vessels, M. Lukáčová-Medviďová, Anna Zaušková, Proceedings of ICIAM 2007, Zurich 2007
  • Numerical study of shear-dependent non-Newtonian fluids in compliant vessels,M. Lukacova, Anna Zaušková , Report TUHH, 2007
  • Mathematical models of flow in elastic tubes, Journal of Electrical Engineering, Vol. 55, No 12/s, 2004, 32-35

  • Luka Grubisic, Vadim Kostrykin, Konstantin A. Makarov, Kresimir Veselic, Stephan Schmitz, Diagonalization of indefinite saddle point forms, in "Analysis as a Tool in Mathematical Physics: in Memory of Boris Pavlov" K. Kurasov, A. Laptev, S. Naboko and B. Simon (eds), Operator Theory: Advances and Applications 276, 2020 ( ISBN 978-3-030-31530-6), arXiv 1710.05105.
  • On the weak solution of the fluid-structure interaction problem for shear-dependent fluid (with M.Lukacova, S. Necasova), Recent Developments of Mathematical Fluid Mechanics edited by H. Amann, Y. Giga, H.Kozono, H.Okamoto and M.Yamazaki, Series of Advanced in Mathematical Fluid Mechanics, Birkhauser Verlag, ISBN 978-3-0348-0939-9, © 2016 (accepted 2014)
  • Fluid-structure interaction for shear-dependent fluids non-Newtonian fluids, Topics in mathematical modeling and analysis, (Hundertmark-Zaušková, M. Lukáčová-Medvid'ová, G. Rusnakova), Jindrich Necas Center for Mathematical Modeling, Lecture notes, Vol. 7, Part IV, 2012, 109-158

  • A Dataset of Reconstructed Carotid Bifurcation Lumen and Plaque Models with Centerline Tree and Simulated Hemodynamics (2.0.0), Eulzer, P., Richter, K., Probst, T., Hundertmark, A., & Lawonn, K. (2024) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.10695923

The publication list of the working group can be found on SciPort RLP.