Prof. Dr. Axel Klar


Building: 48
Room: 575
67663 Kaiserslautern

P.O. Box: 3049
67653 Kaiserslautern


Tel.: +49 631 205 3996

Fax: +49 631 205 4986


Research interests


  • Asymptotic-induced numerical methods for kinetic and hyperbolic equations 
  • Dynamics on networks
  • Mesh-free particle methods in fluid dynamics
  • Moment methods for  kinetic and transport equations 
  • Interacting particle systems and mean-field limits


  • Socioeconomics: modeling and simulation of traffic flow and pedestrian dynamics  
  • Biology: cell motion in tissues and radiation therapy
  • Technology: : fiber dynamics and non-woven textiles, nanotechnology


MathSciNet:  List of publications

MathSciNet:  Author ID

Web of Knowledge: Researcher ID

Scopus: Scopus ID

Google scholar: Google scholar ID


Links to my publications and preprints:


  1.  R. Borsche, A. Klar, Moment methods for kinetic traffic flow and a  class of  macroscopic traffic models, to appear in M3AS, 2024
  2. R. Borsche, A. Klar, A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Non-local Prigogine-Herman Model,  SIAM Appl. Math. 84, 1, 139-164, 2024


  1. S. Tiwari, A. Klar, A mesh-free particle method for continuum modelling of granular flow, Journal of Computational and Applied Mathematics 438, 115529, 2024
  2. I. Akramov, R. Borsche, N. Eckhard and A. Klar, Interface layers and coupling conditions on networks for linearized kinetic BGK equation, Kinetic and related models, doi: 10.3934/krm.2023029, 2023
  3. P.S. Abdul Salam, S. Tiwari, A. Klar, S. Sundar, A numerical investigation of pedestrian dynamics based on rational behaviour in different density scenarios, Physica A:  Statistical mechanics and its applications, 624, 128933, 2023
  4. P.S. Abdul Salam, W. Bock, A. Klar, S. Tiwari, Coupling pedestrian flow and disease contagion models, to appear in Modelling and simulation in Science, engineering and technology, edts. N. Bellomo, L. Gibelli, Springer Nature 2023


  1. S. Tiwari, A. Klar, G. Russo, A meshfree arbitrary Lagrangian-Eulerian method for the BGK model of the Boltzmann equation with moving boundaries, J. Comp. Phys. 458, 111088, 2022
  2. S. Tiwari, A. Klar, G. Russo, Modeling and simulations of moving droplet in a rarefied gas, International Journal of Computational Fluid Dynamics 35, 666-684, 2022
  3. R. Borsche, A. Klar, M. Zanella, Kinetic-controlled hydrodynamics for multilane traffic flow with driver-assist vehicles, Physica A 587, 126486, 2022
  4. M.W. Hlawitschka, S. Tiwari, J. Kwizera, H.-J. Bart, A. Klar, Simulation of fluid particle cutting: validation and case study, Differ. Equ. Dyn. Syst. 30, 363-382, 2022.


  1. P.S. Abdul Salam, W. Bock, A. Klar, S. Tiwari, Disease contagion models coupled to crowd motion and mesh-free simulation, M3AS, 2021
  2. R. Borsche, A. Klar, Asymptotic methods for kinetic and macroscopic equations on networks, Trails in kinetic theory, Sema-Semai, 2021
  3.  M. Rein, J. Mohring, T. Damm, and A. Klar, Model order reduction of hyperbolic systems focusing on district heating networks, J. Franklin Institute, 2021
  4. G. Corbin, A. Klar, C. Surulescu, C. Engwer, M. Wenske, J. Nieto, J. Soler, Modeling glioma invasion with anisotropy and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis, M3AS, 31(1), 177-222, 2021


  1. M. Rein, J. Mohring, T. Damm, and A. Klar, Optimal control of district heating networks using a reduced order model, Optimal control, applications and methods 41 (4), 1352-1370, 2020
  2. S. Tiwari, A. Klar, G. Russo, Interaction of rigid body motion and rarefied gas dynamics based on the BGK model, Mathematics in Engineering, 2,2, 203-229, 2020
  3. P. Goswami, T. Baier, S. Tiwari, C. Lv, S. Hardt and A. Klar, Drag force on spherical particle near a plane wall in rarefied gas. J. Fluid Dyn. 883, A47, 2020
  4. M. Rein, J. Mohring, T. Damm, and A. Klar, Stability preserving model order reduction for district heating networks, Progress in Industrial Mathematics at ECMI 2018, Springer 2020
  5. M.K. Mahato, A. Klar, S. Tiwari, Modelling and Simulation of macroscopic pedestrian flow models, Progress in Industrial Mathematics at ECMI 2018, Springer 2020
  6. A. Meurer, A. Weber, H.-J. Bart, A. Klar, Experimental Validation of a Microscopic Ellipsoidal Particle Model immersed in Fluid Flow, The Nepali Mathematical Science Report, 36 (1-2), 27-37, 2020.


  1. A. Klar, Interacting fiber structures: mathematical aspects and applications, Rivista di Matematica della Università di Parma, 10, 2, 199-268, 2019 
  2. F. Baus, A. Klar, N. Marheineke, R. Wegener, Low-Mach and slenderness limit for elastic Cosserat rods and its numerical investigation, Asymptotic Analysis, 2019
  3. A.Klar, S.Tiwari, A multi-scale particle methods for mean-field equations: the general case,  SIAM Multiscale Mod. Simul. 17 (1), 233-259, 2019 
  4.  L. Müller, A. Klar, F. Schneider, A numerical comparison of the method of moments for the population balance equation, Mathematics and Computers in Simulation 65,  26-55, 2019
  5. R. Borsche, A. Klar, F. Schneider, Numerical methods for mean field and moment models for pedestrian flow, Crowd Dynamics Volume 1 - Theory, Models, and Safety Problems, N. Bellomo and L. Gibelli Eds., Birkhäuser-Springer, MSSET Series, 2019
  6. R. Borsche, A. Klar, F. Schneider, Kinetic and moment models for cell motion in fiber structures, Active Particles Volume 2, Theory,Models, and Applications, N. Bellomo, P. Degond and E. Tadmor Eds., Birkhäuser-Springer, MSSET series, 2019
  7. S. Tiwari, A. Klar, G. Russo,  A mesh-free method for  the BGK model for rarefied gas dynamics,  Int. J. Adv. Eng. Sciences and Appl. Math. 11, 3, 180-197, 2019
  8. M. Rein, J. Mohring, T. Damm, A. Klar, Reduction of a district heating model using network decomposition, Proceedings in Applied Mathematics and Mechanics, DOI: 10.1002/pamm.201900038


  1. R. Borsche, A.Klar A nonlinear discrete-velocity relaxation model for traffic flow, SIAM J. Applied Mathematics, 78 (5), 2891-2917, 2018
  2. R. Borsche, A. Klar, Kinetic layers and coupling conditions for macroscopic equations on networks, SIAM Scientific Computing 40 (3), 1784-1808, 2018
  3. R. Borsche, A. Klar, Kinetic layers and coupling conditions for nonlinear scalar equations on networks, Nonlinearity 31, 351, 2018
  4. G. Corbin, A. Hunt, A. Klar, F. Schneider, C. Surulescu Higher-order models for glioma invasion: from a two-scale description to effective equations for mass density and momentum, M3AS 28 (9), 1771-1800, 2018
  5. N.K. Mahato, A. Klar, S. Tiwari, Particle methods for multi-group pedestrian flow, Appl. Math. Modeling 53, 447-461, 2018 
  6. T. Baier, S. Tiwari, S. Shrestha, H. Hardt, A. Klar, Thermophoresis of Janus particles at large Knudsen numbers, Physical Review Fluids 3, 094202, 2018
  7. N. K. Mahato, A. Klar, S. Tiwari, A meshfree particle method for a vision-based macroscopic pedestrian model, Int. J. Adv. Eng. Sci. Appl.Math 10, 1, 41-53, 2018
  8. J. Bender, A. Klar, and J. Kuhnert, Towards a unified Lagrangian multiscale model for interacting particles, Proceedings in Applied Mathematics and Mechanics,  DOI: 10.1002/pamm.201800209, 2018
  9. M. Rein, J. Mohring, T. Damm, and A. Klar, Parametric model order reduction for district heating networks, Proceedings in Applied Mathematics and Mechanics, DOI:10.1002/pamm.201800192, 2018


  1. L. Kreusser, A. Klar,  O. Tse, Trend  to equilibrium for a delay mean field equation,  SIAM Math. Anal. 49 (4), 3277-3298, 2017
  2. R. Borsche, A. Klar,C. Nessler, A. Roth, O. Tse, A retarded mean field approach for interacting fiber structures, SIAM Multi-scale Mod. Simul. 15 (3), 1130-1154, 2017
  3. R. Borsche, A. Klar, T.N.H. Pham, Nonlinear flux-limited  models for chemotaxis on networks,  NHM 12 (3), 381-401,2017
  4. P. Suchde, J. Kuhnert, S. Schroeder, A. Klar, A flux conserving meshfree method for conservation laws, Int. J. Num. Meth. Eng., 112, 238-256, 2017
  5. L. Müller, A. Meurer, F. Schneider, A. Klar, A numerical investigation of flux-limited approximations for pedestrian dynamics, M3AS 27 (6), 1177-1197, 2017
  6. M. Hack, A.Klar, J. Orlik, Design optimization in periodic structural plates under the constraint of anisotropy, ZAMM 97, 1220-1235, 2017
  7. A. Weber, H.-J. Bart, A. Klar, Simulating spiraling bubble movement in the EL approach, OJFD 7, 288-309, 2017


  1. S. Gramsch, A. Klar, G. Leugering, N. Marheineke, C. Nessler, C. Strohmeyer, R. Wegener. Aerodynamic web forming: Process simulation and material properties. Journal of Mathematics in Industry, 6:13, 2016.
  2. R. Borsche, A. Klar, A. Meurer, O. Tse, Mean field models for interacting ellipsoidal particles, Computers and Mathematics with Applications 72 (3), 704-719, 2016
  3. J. Ritter, A. Klar, F. Schneider, Partial moment minimum entropy models for kinetic chemotaxis equations in one and two dimensions, JCAM, 306, 300-315, 2016
  4. R. Borsche, A. Klar, T.N.H. Pham, Kinetic and related macroscopic models for chemotaxis on networks, M3AS 26 (6), 1219-1242, 2016
  5. A. Pandey, A. Klar, S. Hardt, S. Tiwari, Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method, Computers and Fluids 127, 174-181, 2016
  6. J. A. Carrillo,  A. Klar, A. Roth, Single to double mill small noise transition via Semi-Lagrangian Finite volume Methods,  Comm. Math. Sci. 14 (4), 1111-1136, 2016
  7. S. Tiwari, A. Klar, S. Hardt, Numerical simulation of wetting phenomena by meshfree particle method, Journal of Computational and Applied Mathematics 292, 469-485, 2016
  8. S. Tiwari, A. Klar, S. Hardt, A mesh-free method for simulations of dynamic wetting, Progress in Industrial Mathematics at ECMI 2014, G. Russo, V. Capasso, G. Nicosia, V. Romano Eds. 2016.
  9. A. Klar, C. H. Neßler, C. Strohmeyer, Construction of virtual non-wovens, Progress in Industrial Mathematics at ECMI 2014, G. Russo, V. Capasso, G. Nicosia, V. Romano Eds. 2016.


  1. S. Shresta, S. Tiwari, A. Klar, S. Hardt, Numerical simulation of a moving rigid body in rarefied gas, J. Comp. Phys. 292, 239-252, 2015
  2. A. Klar, O. Tse, An entropy functional and explicit decay rates for a nonlinear partially dissipative hyperbolic system, ZAMM 95 (5),  469-475, 2015
  3. S. Göttlich, A. Klar, S. Tiwari, Complex material flow problems: A multi-scale model hierachy and particle methods, J. Eng. Math. 92, 15-29, 2015
  4.  S. Shresta, S. Tiwari, A. Klar, Comparison of numerical solution of the Boltzmann equations and the Navier-Stokes equations for a moving rigid circular body in a micro cavity,  Int. J. Adv. Eng. Sci. Appl. Math. 7, 38-50, 2015


  1. R. Borsche, A. Klar, Flooding in urban drainage systems: Coupling hyperbolic conservation laws for sewer systems and surface flow, International Journal for Numerical Methods in Fluids, 76 (11), 789-810, 2014
  2. F. Schneider, M. Frank, A. Klar, Higher order mixed moment approximations for the Fokker Planck equations in 1-D, SIAM Appl. Math. 74 (4), 1087-1114, 2014
  3. A.  Klar, F. Schneider, O. Tse, Maximum entropy models for stochastic dynamic systems on the sphere and associated Fokker-Planck equations, Kin. Rel. Models 7 (3), 509-529, 2014
  4. L. Bonilla, A. Klar, S. Martin, Higher order averaging of a  Fokker-Planck equation for Fiber Lay-down Processes, SIAM Appl. Math. 74 (2), 366-391, 2014
  5. A. Roth, A. Klar, B. Simeon, E. Zharovsky, A semi-Lagrangian finite volume method for a 3-D Fokker-Planck equations associated to stochastic dynamical systems on the sphere, J. Scientific Comp., 61 (3), 513-532, 2014
  6. A. Klar, S. Tiwari, A multi-scale  meshfree particle method for macroscopic mean field  interacting particle models, SIAM Multiscale Mod. Sim. 12 (3),  2014
  7. R. Borsche, A. Klar, S. Kühn, A. Meurer, Coupling traffic flow networks to pedestrian motion, Math. Methods Models Appl. Sci. 24 (2), 359-380, 2014
  8. R. Borsche, S. Göttlich, A.Klar, P.Schillen, The scalar Keller-Segel model on networks, Math. Methods Models Appl. Sci. 24 (2), 221-247, 2014
  9. R. Etikyala, S. Göttlich, A. Klar, S. Tiwari, Particle methods for pedestrian flow models: from microscopic to non-local continuum models, Mathematical Methods and Models in Applied Sciences 24 (12), 2503-2523, 2014
  10. M. Grothaus, J. Maringer, A. Klar, P. Stilgenbauer, R. Wegener, Application of a three-dimensional fiber lay-down model to non-woven production processes, J. Math. Ind. 4:4, DOI 10.1186/2190-5983-4-4, 2014 
  11. J. Maringer, A. Klar, R. Wegener,  Three-dimensional fiber lay-down model in an industrial application, Progress in Industrial Mathematics at ECMI 2012, 139-146, 2014 
  12. D. Neusius, S. Schmidt, A. Klar, On boundary approximation for simulation of granular flow, in Finite Volumes for complex applications. Elliptic, parabolic and hyperbolic problems, 927-934, Springer Proc. math. Stat 78, Springer, 2014
  13. R. Etikyala, S. Göttlich, A. Klar and S. Tiwari, A macroscopic model for pedestrian flow: comparisons with experimental results of pedestrian flow in corridors and T-junctions, Neural, Parallel & Scientific Computations, 22 (3), 315-330, 2014.


  1. J. Dolbeault, A. Klar, C. Mouhot, C. Schmeiser, Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes, Appl. Math. Res. Express, doi10.1093/amrx/abs015, 2013
  2. S. Göttlich, A. Klar, P. Schindler, A supply chain model with discontinuous fux function, SIAM Appl. Math. 73, 3, 1117-1138, 2013
  3. S.Tiwari, A. Klar, S. Hardt, A. Donkov, Coupled solution of the Boltzmann and Navier-Stokes equations in gas-liquid two phase flow, Computers and Fluids 71, 283-296, 2013
  4. R. Borsche, M. Kimathi, A. Klar, Kinetic derivations of a  Hamilton-Jacobi type traffic flow model,  Comm. Math. Sci.,  11,3, 739-756, 2013
  5. M. Panchatcharam, S. Sundar, V. Vertrivel, A. Klar, S. Tiwari, GPU Computing for meshfree particle method, International Journal of Numerical Analysis and Modeling, Series B4, 3, 394412, 2013
  6. M. Panchatcharam, S. Sundar,  A. Klar, GPU metrics for a linear solver, Neural Parallel Sci. Comput. 21, 3-4, 361-374, 2013
  7. A. Klar, A. Roth, Kinetic Fokker-Planck equations for vehicular traffic and related micro and macro models,  Ind. J. Ind. Appl. Math., 4(1), 19-32, 2013
  8. S. Tiwari, A. Klar, S. Hardt, Simulations of micro channel gas flows with domain decomposition technique for kinetic and fluid dynamic equations,  Domain decomposition methods in science and engineering XXI, LNCSE 98, Springer, 2013 


  1. R. Borsche, M. Kimathi, A.Klar, A class of multiphase traffic theories for microscopic, kinetic and continuum traffic models, Comp. Math. Appl. 64 (9), 2939-2953, 2012
  2. L. Bonilla, A. Klar, S. Martin,  Higher order averaging of linear  Fokker-Planck equations with periodic forcing, SIAM J. Appl. Math. 72 (4), 1315-1342, 2012
  3. A. Klar, J. Maringer, and R.Wegener, A smooth 3-D model for stochastic fiber lay down, Kin. Rel. Models 5,1, 97 - 112, 2012
  4. A. Klar, J. Maringer, and R.Wegener, A 3-D model for stochastic fiber lay down, Math. Methods Models Appl. Sci. 22, 9 2012 
  5. S. Göttlich, A. Klar, Model hierarchies and optimization for dynamic flows on networks, in Modeling and optimization of flows on networks, Lecture notes in mathematics, Springer 2012
  6. A. Pandey, A. Klar, S. Tiwari, Meshfree method for fluctuating hydrodynamics,  Mathematics and Computers in Simulation 82 (11), 2157–2166, 2012
  7. T. Fütterer, A. Klar, R.Wegener, An energy conserving numerical scheme for the dynamics of hyperelastic rods,  International Journal of Differential Equations  201
  8. T. F. Wächtler, J. Kuhnert, M. Attarakih, S. Tiwari, A. Klar and H.-J.Bart, The normalized quadrature method of moments coupled with finite pointset method, International Conference on Particle-based Methods, Fundamentals and Applications Particles, 2011 E. Onate and D.R.J. Owen (Eds), 2012
  9. A. Pandey, A. Klar, S. Tiwari, Meshfree method for the stochastic Landau-Lifshitz Navier-Stokes equations,  International Conference on Particle based Methods, Fundamentals and Applications PARTICLES 2011 E.Onate and D.R.J. Owen (Eds), 2012
  10. M. Grothaus, A. Klar, J. Maringer, P. Stilgenbauer, Geometry, mixing, properties and hypocoercivity of a degenerate diffusion arising in technical textile industry,


  1. M. Gugat, M. Herty, A. Klar, G. Leugering, V. Schleper, Well--posedness of networked hyperbolic systems of balance laws, International Series of Numerical Mathematics, 160, 175-198, Springer, 2011
  2. A.Donkov, S.Tiwari, T.Liang,S.Hardt, A. Klar,W.Ye, Momentum and Mass Fluxes in a Gas confined between periodically structured Surfaces at different Temperatures, Phys. Rev. E, Volume 84,1, 2011 
  3. M. Frank, A. Klar, Radiative Heat Transfer and Applications for Glass Production Processes, in Mathematical models in the manufacturing of glass, ed. A. Fasano, Lecture Notes in Mathematics 2010, 57-134, Springer 2011
  4. S. Tiwari and A. Klar, Coupling of the Navier-Stokes and the Boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity, in Lecture Notes in computational Science and engineering 79, 155, eds. M. Griebel, M.A. Schweitzer, Springer 2011


  1. M. Frank, A. Klar, R. Pinnau, Optimal Control of Glass Cooling Using Simplified PN Theory, Transport Theory and Statistical Physics, 39 (2), 282, 2010
  2. A. Carrillo, A. Klar, S. Martin, S. Tiwari, Self-propelled interacting particle systems with roosting force, Math. Methods Models Appl. Sci. 20, Suppl., 1533-1552, 2010
  3. M. Attarakih, M. Jaradat, H.-J. Bart, J. Kuhnert, C. Drumm, S. Tiwari, V.K. Sharma, A. Klar, A multivariate sectional quadrature method of moments for the solution of the population balance, in G.B. Ferrais S. Pierucci, editor, Proceed. 20th ECSAPE, pages 1551-1556. Elsevier, Amsterdam, 2010


  1. G. Thoemmes, J. Becker, M. Junk,D. Kehrwald, A. Klar,K. Steiner, A. Wiegmann, Numerical investigation of a combined lattice Boltzmann-level set method for three-dimensional multiphase flow, International Journal of Computational Fluid Dynamics, 23 (10), 687, 2009
  2. M. Herty, A. Klar, S. Motsch, F. Olawsky, A smooth model for fibre lay-down processes and its diffusion approximation, KRM 2 (3), 480-502, 2009
  3. S. Tiwari, A. Klar, S. Hardt, A particle-particle hybrid method for kinetic and continuum equations,  JCP 228,7109-7124, 2009
  4. G. Thömmes, J. Becker, M. Junk,D. Kehrwald, A. Klar,K. Steiner, A. Wiegmann, A Lattice Boltzmann Method for immiscible multiphase flow simulations using the Level Set Method, JCP 228, 1139-1156, 2009
  5. A. Klar, N. Marheineke, and R.Wegener, Hierarchy of mathematical models for production processes of technical textiles, ZAMM, 89(12), 941-961, 2009
  6. A. Klar, P. Reuterswärd, M. Seaid, A Semi-Lagrangian method for a Fokker-Planck equation describing fibre dynamics,  J.  Scientific Computing 38 (3), 349-367, 2009
  7. S. Hardt, S. Tiwari, A. Klar, Momentum Transfer to nanoobjects  between Isothermal Parallel Plates, Microfluidics and Nanofluidics, 6 (4), 489-498, 2009
  8. A. A. Donkov, S. Hardt, S. Tiwari and A. Klar, Coupling of heat and momentum transfer between nanostructured surfaces, Proc. ASME 2009 2nd Micro/Nanoscale Heat and Mass Transfer International Conference, Shanghai, China, 2009
  9. D. Wright, M. Frank, A. Klar, The Minimum Entropy Approximation to the Radiative Transfer Equation, Proceedings of Symposia in Applied Mathematics, 67,2, 987-997, AMS 2009
  10. M. Attarakih, M. Jaradat, C. Drumm, H. - J. Bart, S. Tiwari, V. K. Sharma, J. Kuhnert and A. Klar, Solution of the population balance equation using the one primary and One secondary method (OPOSPM), Computer-Aided Chemical Engineering, 26,, 1333, J. Jezowski and J. Thullie (Eds), Elsevier, 2009
  11. M. Attarakih, M. Jaradat, C. Drumm, H. - J. Bart, S. Tiwari, V. K. Sharma, J. Kuhnert and A. Klar, A multivariate Population Balance Model for Liquid Extraction Column, Computer-Aided Chemical Engineering, 26,, 1339, J. Jezowski and J. Thullie (Eds), Elsevier, 2009
  12. V.K. Sharma, S. Tiwari, M. Attarakih, M. Jaradat, A. Klar, J. Kuhnert and H.-J. Bart, Simulation of two phase flow with incorporated population balance equation using a meshfree method, in J. Jezowski / J. Thullie (Eds.), 19th European Symposium on Computer Aided Process Engineering ESCAPE 19. Poland: Elsevier, 2009


  1. P. Degond, S. Goettlich,  A. Klar, M. Seaid, A. Unterreiter, Derivation of a kinetic model from a stochastic particle system, Kinetic and Related models (KRM), 1(4), pp. 557-572, 2008
  2. T. Goetz, A. Klar, A. Unterreiter, R. Wegener, Numerical evidence for the non-existence of solutions to the equations describing rotational fiber spinning,  MMMAS 18,10,1829-1844, 2008 
  3. M. Grothaus, A. Klar, Ergodicity and rate of convergence for a nonsectorial fiber lay-down process , SIAM Math. Anal, 40,3,2008
  4. A. Klar, M. Seaid, G. Thoemmes, Lattice Boltzmann Simulation of Depth-Averaged Models in Flow Hydraulics, International Journal of Computational Fluid Dynamics 22,507-522,2008  
  5. A. Fuegenschuh, S. Goettlich, M. Herty, A. Klar, A. Martin, A discrete optimization approach to Large Scale Supply Networks based on Partial Differential Equations, SIAM Scient. Computing 30, 3, 1490-1507 2008
  6.  T. Goetz, A. Klar and A. Unterreiter, Asymptotics of fiber spinning equations, Progress in Industrial Mathematics at ECMI 2006, L.L. Bonilla, M. Moscoso, G. Platero, J.M. Vega (eds.), Springer 2008, 697-702
  7. S. Tiwari, C. Drumm, V.K. Sharma, J. Kuhnert, M. M. Attarakih, A. Klar and H.-J. Bart, A Meshfree CFD-Population Balance Equation Coupled Model, Proc. 6th International Conference on Computational Fluid Dynamics in the Oil / Gas, Metallurgical and Process Industries CFD 2008, Trondheim, Norway, 2008


  1. L. Bonilla,T. Goetz, A. Klar, N. Marheineke, R. Wegener, Hydrodynamic limit of a Fokker--Planck equation describing fiber lay--down processes, SIAM Appl. Math. 68, 3, 648-665, 2007 
  2. T. Goetz, A. Klar, N. Marheineke, R. Wegener, A Stochastic Model and Associated Fokker-Planck Equation for the Fiber Lay-down Process in Nonwoven Production Processes, SIAM Appl. Math. 67, 6, 1704-1717, 2007 
  3. M. Frank, M. Frank, A. Klar, E. Larsen, S. Yasuda, Time -dependent Simplified PN Approximation to the Equations of radiative transfer, JCP 226 (2), 2289-2305, 2007 
  4. M. Banda, A. Klar, M. Seaid, Lattice Boltzmann relaxation methods for coupled convection and radiation systems, Journal of Computational Physics 226, 2, 1408, 2007
  5. M. Frank, H. Hensel, A. Klar, Toward fast and accurate deterministic methods for dose calculation in electron radiotherapy, IMECS 2007, 2361-2365
  6. M. Banda, A. Klar, L. Pareschi, M. Seaid, Lattice Boltzmann type relaxation systems and relaxation schemes for the incompressible Navier Stokes equations, Mathematics of Computation 77, 943-965, 2007
  7. P. Degond, S. Goettlich, M. Herty, A. Klar, A network model for supply chains with multiple policies, SIAM Multiscale Modeling and Simulation 6(3), pp. 820-837, 2007
  8. E. Schneider, M. Seaid, J.Janicka, A. Klar, Validation of simplified PN models for radiative transfer in combustion systems, Comm. Num. Meth. Eng. 24, 2, 85-96, 2007
  9. M. Herty, A. Klar, B. Piccolli, Existence of solutions for supply chain models based on partial differential equations, SIAM J. Math. Anal. 39 (1), 160-173, 2007 
  10. M. Frank. H. Hensel, A. Klar, A fast and accurate moment method for the Fokker-Planck equation and Applications to Electron Radiotherapy, SIAM Appl. Math. 67 (2), 582-603, 2007 
  11. M. Gugat, M. Herty, A. Klar, G. Leugering, Conservation law constrained optimizaton based upon front-tracking, MMAN 40 (5), 939-960, 2007 
  12. M. Herty, A. Klar, A.K. Singh, P. Spellucci, Smoothed Penalty Algorithms for Optimization of Nonlinear Models, COAP 37 (2), 157-176, 2007 
  13. M. Herty, A. Klar and A.K. Singh, An ODE traffic network model, Journal of Computational and Applied Mathematics, 203 (2), 419-436, 2007


  1. C. Kirchner, S. Goettlich, M. Herty, A. Klar, Optimal control for continuous supply network models, NHM 1 (4), 675-688, 2006
  2. M. Herty, C. Kirchner, A. Klar, Instantaneous Control For Traffic Flow, MMAS 30 (2), 153-169, 2006 
  3. M. Frank, B. Dubroca, A. Klar, Partial moment entropy approximation to radiative heat transfer, JCP 218 (1), 1-18, 2006 
  4. M. Herty, R. Illner, A. Klar, V. Panferov, Qualitative Properties of Solutions of Systems of Fokker-Planck Equations in Multilane Traffic Flow, TTSP 35 (1-2), 31-54, 2006 
  5. S. Goettlich, M. Herty, A. Klar, Modelling and Optimization of supply chains on complex networks, CMS, 4(2), 315-330, 2006 
  6. M. Banda, M. Herty, A. Klar, Coupling conditions for gas networks governed by the isothermal Euler equations, NHM 1(2), 295-314, 2006
  7. M. Banda, M. Herty, A. Klar, Gas flow in pipeline networks, NHM 1(1), 41-56, 2006
  8. I. Teleaga, M. Seaid, I. Gasser, A. Klar, J. Struckmeier, Radiation models for thermal flows at low Mach numbers, JCP 215 (2), 506-525, 2006
  9. M.K. Banda, Wen-An Yong, A. Klar, A Stability Notion for Lattice Boltzmann Equations, SISC 27,(6), 2098-2111, 2006 
  10. A. Fuegenschuh, M. Herty, A. Klar, A. Martin, Combinatorial and Continuous Models for the Optimization of Traffic Flows on Networks, SIOPT 16(4), 1155-1176, 2006
  11. M. Seaid, A. Klar, Asymptotic-Preserving Schemes for Unsteady Flow Simulations, J. Computers and Fluids 35 (8-9), 872-878, 2006
  12. M. Banda, M. Junk, A. Klar, Kinetic-based numerical schemes for incompressible Navier- Stokes equations, J. Computers and Fluids, 35 (8-9), 879-887, 2006


  1. S. Goettlich, M. Herty, A. Klar,Network models for supply chains, CMS 3(4), 545-559, 2005 
  2. M. Herty, A. Klar, L. Pareschi, General kinetic models for vehicular traffic flow and Monte Carlo methods, Computational methods in applied mathematics 5(2), 155-169, 2005
  3. M. Junk, A. Klar, L.S. Luo, Asymptotic Analysis of the Lattice Boltzmann Equation, JCP 210 (2), 676-704, 2005
  4. M. Gugat, M. Herty, A. Klar, G. Leugering, Optimal control for traffic flow networks, JOTA 126 (3), 589-616, 2005
  5. M. Seaid, A. Klar, R. Pinnau, Numerical Solvers for Radiation and Conduction in High Temperature Gas Flows J. Flow Turbulence and Combustion, 75, 173-190, 2005
  6. M. Seaid, A. Klar, Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing Progress in Industrial Mathematics at ECMI 2004, 8, 283-287, 2005
  7. A. Klar, J. Lang, M. Seaid, Adaptive solutions of SP_N-Approximations to radiative heat transfer in glass, Int. J. Thermal Sciences, 44, 1013-1023, 2005


  1. M. Seaid, M. Frank, A. Klar, R. Pinnau and G. Thoemmes, Efficient numerical methods for radiation in gas turbines, J. Comp. Applied Math. 170 (1), 217-239, 2004
  2. R. Turpault, M. Frank, B. Dubroca, A. Klar, Multigroup half space moment approximations to the radiative heat transfer equations, JCP, 198 (1), 363-371, 2004
  3. M. Herty, A. Klar, Simplified dynamics and Optimization of Large Scale Traffic Flow Networks, Math. Mod. Meth. Appl. Sci. 14 (4), 579-601, 2004
  4. N. BenAbdallah, I. Gamba, A. Klar, The Milne Problem for High Field Kinetic Equations,SIAM Appl. Math. 64/5, 1709-1736, 2004
  5. A. Klar, R. Wegener, Traffic flow: models and numerics, in Modeling and Computational Methods for Kinetic Equations, Editors: P. Degond, L. Pareschi, G. Russo, Birkhaeuser, 219-259, 2004
  6. B. Dubroca, A. Klar and M. Seaid, Flux Limiters in the Coupling of Radiation and Hydrodynamics Models J. Comp. Appl. Math. 168 (1-2), 425-435, 2004
  7. M. Frank, A. Klar, M. Seaid, R. Pinnau and G. Thoemmes, A comparison of approximate models for radiation in gas turbines Progress in Computational Fluid Mechanics (PCFD) 4 (3-5), 191-197, 2004
  8. M. Banda, M. Seaid A. Klar, L. Pareschi, Compressible and Incompressible Limits for Hyperbolic Systems with Relaxation, J. Comp. Appl. Math. 168 (1-2), 41-52, 2004


  1. E. Larsen, G. Thoemmes, A. Klar, New Frequency-Averaged Approximations to the Equations of Radiative Heat Transfer, SIAM Appl. Math.64 (2), 565-582, 2003
  2. M. Herty, A. Klar, Modeling, Simulation and Optimization of Traffic Flow Networks, SIAM Sci. Comp. 25 (3), 1066-1087, 2003 
  3. A. Klar, L. Pareschi, M. Seaid, Uniformly accurate schemes for relaxation approximations to fluid dynamic equations, Appl. Math. Let. 16 (7), 1123-1127, 2003
  4. M. Guenther, A. Klar, T. Materne, R. Wegener, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, SIAM J. Appl. Math. 64 (2), 468-483, 2003
  5. R. Illner, A. Klar, T. Materne, Vlasov-Fokker-Planck models for multilane traffic flow, Comm. Math. Sci. 1 (1), 1-12, 2003 
  6. M. Banda, M. Junk, A. Klar, Kinetic derivation of a finite difference scheme for the incompressible Navier Stokes equation,  J. Comp. Appl. Math., 154 (2), 341-354 , 2003 
  7. J. Greenberg, A. Klar, M. Rascle, Congestion on multilane highways SIAM J. Appl. Math. 63 (3), 818-833, 2003
  8. B. Dubroca, M. Frank, A. Klar, G. Thoemmes, A half space moment approximation to the radiative heat transfer equations, Z. Angew. Math.Mech., 83 (12), 853-858 2003
  9. M. Seaid, A. Klar, Efficient Preconditioning of Linear Systems Arising from the Discretization of Radiative Transfer Equation, Challenges in Scientific Computing, Berlin 2002, Lecture Notes in Computational Science and Engineering, 35, 211-236, 2003
  10. R. Illner, A. Klar, T. Materne, On Vlasov-Fokker-Planck type kinetic models for multilane traffic Flow, Rarefied Gas Dynamics: 23rd International Symposium, Whistler 2002, 283-290, 2003
  11. M. Seaid, A. Klar, Generalized numerical approximations for the radiative heat transfer problems in two space dimensions Eurotherm73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 419-429, 2003
  12. A. Klar, G. Thoemmes, Numerical methods for radiative heat transfer in diffusive regimes, in IMA Volumes in Mathematics and its Applications 135: Transport in Transition Regimes Springer-Verlag, New York, 199-216, 2003


  1. B. Dubroca, A. Klar, A half moment model to take into account strong kinetic non-equilibrium, C.R.Acad.Sci.Paris, Ser. I 335 (8), 699-704, 2002
  2. B. Dubroca, A. Klar, Half Moment closure for radiative transfer equations, J. Comp. Phys., 180 (2), 584-596, 2002 
  3. E. Larsen, G. Thoemmes,M. Seaid,T. Goetz, A. Klar, Simplified PN approximations to the equations of radiative transfer and applicatons to glass manufacturing, J. Comp. Phys., 183 (2), 652-675, 2002 
  4. R. Illner, C.Stoica, A. Klar, R. Wegener, Kinetic equilibria in traffic flow models, TTSP, 31 (7), 615-634, 2002 
  5. A. Klar, A. Unterreiter, Uniform stability of a finite difference scheme for transport equations in diffusive regimes, SIAM J. Num. Anal. 40 (3), 891-913, 2002 
  6. A. Aw, A. Klar, T. Materne, M. Rascle, Derivation of continuum flow traffic models from microscopic Follow the leader models, SIAM J. Appl. Math. 63 (1), 259-278, 2002 
  7. M. Guenther, A. Klar, T. Materne, R. Wegener, An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations, Math. Comp. Modelling 35 (5-6), 591-606, 2002 
  8.  P. Degond, A. Klar, A relaxation approximation for transport equations in the diffusive limit, Appl. Math. Lett. 15(2), 131--135, 2002
  9.  A. Klar, M. Herty, Modelling of Traffic Flow Networks, in Modelisation du trafic: Actes du groupe de travail 2002, Actes No. 97, Les Collections des L'Inr ets, Editor M. Arion, F. Boillot, J.-P. Lebacque
  10. G. Thoemmes, R. Pinnau, M. Seaid, T. Goetz, A. Klar, Numerical Methods and Optimal Control for Glass Cooling Processes TTSP 31 (4-6), 513-529, 2002
  11. M. Banda, M. Junk, A. Klar, A limiter based on Kinetic theory TTSP, 31 (4-6), 491-512, 2002


  1. A. Klar, C. Schmeiser,Numerical Passage from Radiative Heat Transfer to Nonlinear Diffusion Models, Math. Meth. Mod. Appl. Sci. 11 (5), 749-767, 2001
  2. A. Klar,  M. Seaid, High-Order Relaxation Methods for Incompressible Navier-Stokes Equations Numerical Mathematics and Advanced Applications, 79-89, 2001


  1. M. Junk, A. Klar, Discretization for the incompressible Navier Stokes equations based on the Lattice-Boltzmann method, SIAM J. Sci. Comp., 22 (1), 1-19, 2000
  2. A. Klar, R. Wegener, Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic, SIAM J. Appl. Math. 60 (5), 1749-1766, 2000
  3. S. Albeverio, A. Klar, Longtime Behaviour of Stochastic Hamiltonian Systems, Potential Analysis 12, 281-297, 2000 
  4. A. Klar, R. Wegener, Kinetic Traffic Flow Models, in 'Modeling in Applied Sciences: A kinetic theory approach', Editors N. Bellomo, M. Pulvirenti, Birkhäuser, 263-317, 2000 
  5. A. Klar, H. Neunzert, J. Struckmeier, Transition from Kinetic Theory to Macroscopic Fluid Equations: A Problem for Domain Decomposition and a Source for New Algorithms, TTSP 29 (1-2), 93-106, 2000
  6. A. Klar, R. Wegener, Vehicular Traffic: From Microscopic to Macroscopic Description, Proceedings of the 5th MAFPD workshop, Maui, Hawaii 1998, TTSP 29 (3-5), 479-493, 2000


  1. A. Klar, An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit, SIAM J. Num. Anal., 36 (5), 1507-1527, 1999
  2. R. Illner, A. Klar, H. Lange, A. Unterreiter, R. Wegener, A Kinetic Model for Vehicular Traffic: Existence of stationary solutions, J. Math. Anal. Appl. 237 (2), 622-643, 1999
  3. A. Klar, Relaxation Scheme for a Lattice Boltzmann-type Discrete Velocity Model and Numerical Navier Stokes Limit, J. Comp. Phys. 148 (2), 416-432, 1999
  4. A. Klar, R. Wegener, A Hierarchy of Models for Multilane Vehicular Traffic I: Modeling, SIAM J. Appl. Math. 59 (3), 983-1001, 1999
  5. A. Klar, R. Wegener, A Hierarchy of Models for Multilane Vehicular Traffic II: Numerical Investigations, SIAM J. Appl. Math. 59 (3), 1002-1011, 1999
  6. A. Klar, A Numerical Method for Kinetic Semiconductor Equations in the Drift Diffusion Limit, SIAM J. Sci. Comp., 20 (5), 1696-1712, 1999


  1. A. Klar, An Asymptotic Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit, SIAM J. Num. Anal. 35 (3), 1073-1094, 1998
  2. A. Klar, Asymptotic Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations, SIAM J. Sci. Comp. 19 (6), 2032-2050, 1998
  3. A. Klar, N. Siedow, Boundary Layers and Domain Decomposition for Radiative Heat Transfer and diffusion Equations: Applications to Glass Manufacturing Processes, Eur. J. Appl. Math. 9-4, 351-372, 1998
  4. S. Tiwari, A. Klar, An Adaptive Domain Decomposition Procedure for Boltzmann and Euler Equations, J. Comp. Appl. Math. 90 (2), 223-237, 1998
  5. A. Klar, Asymptotic Analysis and Coupling Conditions for Kinetic and Hydrodynamic Equations, Comp. Math. Appl., Vol. 35 (1-2), 127-137, 1998
  6. A. Klar, A Numerical Method for Nonstationary Transport Equations in Diffusive Regimes Proceedings of the 15. International Conference on Transport Theory 1997 in Goeteborg, TTSP 27 (5-7), 653-666, 1998


  1. A. Klar, R. Wegener, Enskog-like Kinetic Models for Vehicular Traffic , J. Stat. Phys., 87, (1-2), 91-114, 1997 
  2. Y.Arkipov, A. Klar, O. Mingalyov, V.Vedenyapin, A Class of Invariants for the Boltzmann Equation and the Broadwell Model, Eur. J. Mech./B, 16, 3, 387-399, 1997
  3. A. Klar, H.Neunzert, J. Struckmeier, Particle Methods and Domain Decomposition, Proceedings of the 20. International Symposium on Rarefied Gas Dynamics 1996 in Bejing, ed. by C. Shen, Peking University Press, 263-272, Beijing, 1997


  1. A. Klar, R. Kuehne, R. Wegener, Mathematical Models for Vehicular Traffic, Surv. Math. Ind., 6, 215-239, 1996
  2. A. Klar, R. Wegener, A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model, Transp. Theory Stat. Phys., 25(7), 785-798, 1996 
  3. A. Klar, Domain Decomposition for Kinetic Problems with Noneqilibrium States, Eur. J. Mech., B/Fluids, 15, 2, 203-216, 1996
  4. A. Klar, H.Neunzert, J. Struckmeier, Particle Methods: Theory and Applications, ICIAM 95: proceedings of the Third International Congress on Industrial and Applied Mathematics held in Hamburg, Germany, 1995, ed. by K. Kirchgaessner, O. Mahrenholtz, R. Mennicken, Berlin: Akad. Verl., (Mathematical Research, Vol. 87) 281-306, 1996


  1. A. Klar, Computation of nonlinear functionals in Particle Methods, Computing 55 (3), 207-221, 1995
  2. F. Golse, A. Klar, A Numerical Method for Computing Asymptotic States and Outgoing Distributions for a Kinetic Linear Half Space Problem,  J. Stat. Phys. 80 (5-6), 1033-1061, 1995 
  3. A. Klar, Convergence of Alternating Domain Decomposition Schemes, Math. Meth. Appl. Sci. 18 (8), 649-670, 1995  
  4. A. Klar, Domain Decomposition and Coupling Conditions for Kinetic and Hydrodynamic Equations, Numerical Treatment of Coupled Systems, ed. by W. Hackbusch, G. Wittum, Vieweg, Braunschweig, Notes Numer. Fluid Mech. 51, 128-138, 1995
  5. S.Albeverio, J. Gaines, A. Klar, Longtime Behaviour of Nonlinear Hamiltonian Systems with a Stochastic Force, Stochastic Processes, Physics and Geometry II, Proceedings Locarno, Switzerland, 24 - 29 June 1991, S. Albeverio, U.Cattaneo, D.Merlini (Edts), 14-28, World Scientific, Singapore 1995 


  1. Y.Arkipov, A. Klar, V.Vedenyapin, On the Connection of Entropy and Stationary Distributions, J. Stat. Phys. 77 (5-6), 1027-1037, 1994    
  2. S. Albeverio, A. Klar, Longtime Behaviour of Nonlinear Stochastic Oscillators, J. Math. Phys. 35 (8), 4005-4027, 1994    


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