Dr. Alina Chertock

Overview:

Dr. Alina Chertock is Associate Director of the Center for Research in Scientific Computation at North Carolina State University where she is a Professor and Department Head of Mathematics.

Dr. Chertock received her Ph.D. in Mathematics from Tel-Aviv University, Israel, in 1999. Her research interests include applied nonlinear partial differential equations, scientific computing, numerical analysis, multiscale models, uncertain phenomena, and experimental asymptotics.

Current Projects:

• Development and Application of Modern Numerical Methods for Nonlinear Hyperbolic Systems of PDEs 9/1/22 – 8/31/25, $369,000

Completed Projects:

• Collaborative Research: Structure Preserving Numerical Methods for Hyperbolic Balance Laws with Applications to Shallow Water and Atmospheric Models 9/1/18 – 8/31/2023, $250,000
• Collaborative Research:  Numerical Methods For Partial Differential Equations Arising In Shallow Water Modeling 9/1/15 – 8/31/19, $250,000

Publications:

• A. Chertock, A. Kurganov, M. Redle and V. Zeitlin, Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD, Journal of Computational Physics, 518 (2024), pp. 113300.
• A. Chertock, M. Herty, A. S. Iskhakov, S. Janajra, A. Kurganov, and M. Lukacova-Medvidova, New high-order numerical methods for hyperbolic systems of nonlinear PDEs with uncertainties, Communications on Applied Mathematics and Computation, (2024) https://doi.org/10.1007/s42967-024-00392-z
• A. Chertock, S. Chu and A. Kurganov, An accurate deterministic projection method for two-dimensional stiff detonation waves, Communications in Mathematics Sciences, 22 (2024), pp. 871-910.
• A. Chertock, A. Kurganov, M. Redle and K. Wu, A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics, SIAM Journal on Scientific Computing, 46 (2024), pp. A1998-A2024.
• A. Chertock and C. Leonard, Simulating partial differential equations with neural network, Proceedings of the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham., (2024).
• A. Chertock, C. Leonard, S. Tsynkov, and S. Utyuzhnikov, Denoising convolution algorithms and applications to SAR signal processing, Communications on Analysis and Computation, 1 (2023), pp. 135-156.
• A. Chertock, S. Chu, and A. Kurganov, Adaptive high-order A-WENO schemes based on a new local smoothness indicator, East Asian Journal on Applied Mathematics, 13 (2023), pp. 576-609.
• C. Wang, A. Chertock, S. Cui, A. Kurganov, and Z. Zhang, A diffuse-domain based numerical method for a chemotaxis-fluid model, Mathematical Models and Methods in Applied Sciences, 33 (2023), pp. 341–375.
• A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, B. Wiebe, Stochastic Galerkin method for cloud simulation. Part II: A fully random Navier-Stokes-cloud model, Journal of Computational Physics, 479 (2023), Paper No. 111987, 24 pp.
• A. Chertock, S. Chu, M. Herty, A. Kurganov, M. Lukacova-Medvidova, Local characteristic decomposition based central-upwind scheme, Journal of Computational Physics, 473 (2023), Paper No. 111718, 24 pp.
• A. Chertock, A. Kurganov, T. Wu and J. Yan, Well-balanced numerical method for atmospheric flow equations with gravity, Applied Mathematics and Computation, 439 (2023), Paper No. 127587, 13 pp.
• A. Chertock, P. Degond, G. Dimarco, M. Lukacova-Medvidova, A. Ruhi, On a hybrid continuum-kinetic model for complex fluids, Partial Differential Equations and Applications, 3 (2022), no. 5, Paper No. 63, 28 pp.
• A. Chertock, A. Kurganov, X. Liu, Y. Liu, and T. Wu, Well-balancing via flux globalization: Applications to shallow water equations with wet/dry fronts, Journal of Scientific Computing, 90 (2022), no. 1, Paper No. 9, 21 pp.
• A. Chertock, S. Chu, and A. Kurganov, Hybrid multifluid algorithms based on the path-conservative central-upwind scheme, Journal of Scientific Computing, 89 (2021), no. 2, Paper No. 48, 24 pp.
• A. Chertock, A. Kurganov, and T. Wu, Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography, Communications in Mathematical Sciences, 18 (2020), pp. 2149–2168.
• A. Chertock, A. Kurganov, J. Miller, and J. Yan, Central-upwind scheme for a non-hydrostatic Saint-Venant system, Proceedings of the XVII International Conference on Hyperbolic Problems: Theory, Numerics and Applications, American Institute of Mathematical Sciences, 10 (2020), pp. 25-42.
• A. Chertock, A. Kurganov, and Y. Liu, Finite-volume-particle methods for the two-component Camassa-Holm system, Communications in Computational Physics, 27 (2020), pp. 480-502.
• X. Liu, A. Chertock, A. Kurganov, and K. Wolfkill, One-dimensional/two-dimensional coupling approach with quadrilateral confluence region for modeling river systems, Journal of Scientific Computing, 81 (2019), pp. 1297-1328.
• A. Chertock, A. Ditkowski, A. Gelb, S. Gottlieb, S. Tsynkov, Preface to the special issue in memory of Professor Saul Abarbanel [Editorial], Journal of Scientific Computing, 81 (2019), pp. 1119–1123.
• A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, and B. Wiebe, Stochastic Galerkin method for cloud simulation, Mathematics of Climate and Weather Forecasting, 5 (2019), pp. 65-106.
• A. Chertock and A. Kurganov, High-resolution positivity and asymptotic preserving numerical methods for chemotaxis and related models, Active Particles, Volume 2. Modeling and Simulation in Science, Engineering and Technology, Springer International Publishing, Birkhauser (2019), pp. 109-148.
• A. Chertock, P. Degond, S. Hecht, and J.-P. Vincent, Incompressible limit of a continuum model of tissue growth with segregation for two cell populations, Mathematical Biosciences and Engineering, 16 (2019), pp. 5804–5835.
• A. Chertock, A. Kurganov, M. Ricchiuto and T. Wu, Adaptive moving mesh upwind scheme for the two-species chemotaxis model, Computers and Mathematics with Applications, 77 (2019), pp. 3172-3185.
• Y. Cheng, A. Chertock, M. Herty, A. Kurganov, and T. Wu, A new approach for designing moving-water equilibria preserving schemes for the shallow water equations, Journal of Scientific Computing, 80 (2019), pp. 538–554.
• X. Liu, A. Chertock, and A. Kurganov, An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces, Journal of Computational Physics, 391 (2019), pp.259-279.
• A. Chertock, A. Kurganov, M. Lukacova-Medvidova, and S. Ozcan, An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions, Kinetic and Related Models, 12 (2019), pp.195-216.
• A. Chertock, M. Herty and S. Ozcan, Well-balanced central-upwind schemes for 2×2 systems of balance laws, Proceedings of the XVI International Conference on Hyperbolic Problems: Theory, Numerics and Applications of Hyperbolic Problems I, Springer, 236 (2018), pp. 345-361.
• A. Chertock, S. Cui, A. Kurganov, S. Ozcan and E Tadmor, Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes, Journal of Computational Physics, 358 (2018), pp. 36-52.
• A. Chertock, C. Tan and B. Yan, An asymptotic preserving scheme for kinetic models with singular limit, Kinetic and Related Models, 11 (2018), pp. 735-756.
• A. Chertock, M. Dudzinski, A. Kurganov and M. Lukacova-Medvidova, Well-balanced schemes for the shallow water equations with Coriolis forces, Numerische Mathematik, 138 (2018), pp. 939-973.
• A. Chertock, Y. Epshteyn, H. Hu and A. Kurganov, High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems, Advances in Computational Mathematics, 44 (2018), pp. 327-350.
• A. Chertock, A. Coco, A. Kurganov and G. Russo, A second-order finite-difference method for compressible fluids in domains with moving boundaries, Communications in Computational Physics, 23 (2018), pp. 230-263.
• Y. Cheng, A. Chertock, and A. Kurganov, A simple finite-volume method on a cartesian mesh for pedestrian flows with obstacles, Finite Volumes for Complex Applications, VIII—methods and theoretical aspects (Lille, 2017), pp. 43-55, Springer Proc. Math. Stat., 199, 2017.
• A. Chertock, S. Cui and A. Kurganov, Hybrid finite-volume-particle methods for dusty gas flows , SMAI Journal of Computational Mathematics 3 (2017), pp. 139-180.
• A. Chertock, A practical guide to deterministic particle methods, Handbook of Numerical Methods for Hyperbolic Problems, Volume 18, 1st Edition, Elsevier, (2017), pp. 177-202.
• A. Chertock, P. Degond and J. Neusser, An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations, Journal of Computational Physics, 335 (2017), pp. 387-403.
• A. Bernstein, A. Chertock and A. Kurganov, Central-upwind scheme for shallow water equations with discontinuous bottom topography, Proceedings of the XV International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Bulletin of the Brazilian Mathematical Society, Springer, 47 (2016), pp. 91-103.
• A. Chertock, S. Cui, A. Kurganov, and T. Wu, Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms, International Journal for Numerical Methods in Fluids, 78 (2015), pp. 355-383.
• A. Chertock, S. Cui, A. Kurganov and T. Wu, Steady state and sign preserving semi-implicit Runge-Kutta methods for ODEs with stiff damping term, SIAM Journal on Numerical Analysis, 53 (2015), pp. 2008-2029.
• A. Chertock, J.-G. Liu and T. Pendleton, Elastic collisions among peakon solutions for the Camassa-Holm equation, Applied Numerical Mathematics, 93 (2015), pp. 30-46.
• J. A. Carrillo, A. Chertock, and Y. Huang, A finite-volume method for nonlinear nonlocal equations with a gradient flow structure, Communications in Computational Physics, 17 (2015), pp. 233-258.
• M. Castro Diaz, Y. Cheng, A. Chertock, and A. Kurganov, Solving two-mode shallow water equations using finite volume methods, Communications in Computational Physics, 16 (2014), pp. 1323-1354.
• A. Chertock, M. Herty and A. Kurganov, An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs, Computational Optimization and Applications, 59, (2014), pp. 689-724.
• A. Chertock, A. Kurganov and Y. Liu, Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients, Numerische Mathematik, 127 (2014), pp. 595-639.
• A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev, Pedestrian flow models with slowdown interactions, M3AS: Mathematical Models and Methods in Applied Sciences, 24 (2014), pp. 249-275.
• A. Chertock, A. Kurganov, Z. Qu and T. Wu, Three-layer approximation of two-layer shallow water equations, Mathematical Modeling and Analysis, 18 (2013), pp. 675-693.
• A. Chertock, J.-G. Liu and T. Pendleton, Convergence of a particle method and global weak solutions for a family of evolutionary PDEs, SIAM Journal on Numerical Analysis, 50 (2012), pp. 1-21.
• A. Chertock, K. Fellner, A. Kurganov, A. Lorz and P. Markowich, Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach, Journal of Fluid Mechanics, Cambridge University Press 2012, 694 (2012), pp. 155-190.
• A. Chertock, J.-G. Liu and T. Pendleton, Convergence analysis of the particle method for the Camassa-Holm equation, Proceedings of the 13th International Conference on`Hyperbolic Problems: Theory, Numerics and Applications”, (Ph. G. Ciarlet and Ta-Tsien Li, eds.), Contemporary Applied Mathematics, 2012, pp. 365-373.
• A. Chertock, A. Kurganov, X. Wang and Y. Wu, On a chemotaxis model with saturated chemotactic flux, Kinetic and Related Models, 5 (2012), pp. 51-95.
• A. Chertock, P. Du Toit and J. E. Marsden, Integration of the EPDiff equation by particle methods, M2AN Mathematical Modelling and Numerical Analysis, 46 (2012), pp. 515-534.
• A. Chertock, C.I. Christov and A. Kurganov, Central-upwind schemes for the Boussinesq paradigm equations in Computational Science and High Performance Computing IV, The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, vol. 115 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer, 2011, pp. 267-281.
• A. Chertock, C. Doering, E. Kashdan and A. Kurganov, A fast explicit operator splitting method for passive scalar advection, Journal of Scientific Computing, 45 (2010), pp. 200-214.
• A. Chertock and A. Kurganov, On splitting-based numerical methods for convection-diffusion equations, in Numerical Methods for Balance Laws, Quaderni di Matematica, Dept. Math., Seconda Univ. Napoli, Caserta, 24 (2009), p. 303-343.
• A. Chertock, A. Kurganov and G. Petrova, Fast explicit operator splitting method for convection-diffusion equations, International Journal for Numerical Methods in Fluids, 59 (2009), pp. 309-332.
• A. Chertock and A. Kurganov, Computing multivalued solutions of pressureless gas dynamics by deterministic particle methods, Communications in Computational Physics, 5 (2009), pp. 565-581.
• A. Chertock and A. Kurganov, A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models, Numerische Mathematik, 111 (2008), pp. 169-205.
• A. Chertock, D. Gottlieb and A. Solomonoff, Modified optimal prediction and its application to a particle-method problem, Journal of Scientific Computing, 37 (2008), pp. 189-201.
• A. Chertock and A. Kurganov, A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries, Communications in Mathematical Sciences, 6 (2008), pp. 531-556.
• A. Chertock, S. Karni and A. Kurganov, Interface tracking method for compressible multifluids, Mathematical Modelling and Numerical Analysis, M2AN, 42 (2008), pp. 991-1019.
• A. Chertock, E. Kashdan and A. Kurganov, Propagation of diffusing pollutant by a hybrid Eulerian-Lagrangian method, Hyperbolic Problems: Theory, Numerics, Applications (Lyon 2006), pp. 371-380, Springer, 2008.
• A. Chertock, A. Kurganov and Yu. Rykov, A new sticky particle method for pressureless gas dynamics, SIAM Journal on Numerical Analysis, 45 (2007), pp. 2408-2441.
• A. Chertock, A. Kurganov and G. Petrova, Finite-volume-particle methods for models of transport of pollutant in shallow water, Journal of Scientific Computing, 27 (2006), pp. 189-199.
• A. Chertock and A. Kurganov, On a practical implementation of particle methods, Applied Numerical Mathematics, 56 (2006), pp. 1418-1431.
• A. Chertock, A. Kurganov and G. Petrova, Fast explicit operator splitting method. Application to the polymer system, Finite Volumes for Complex Applications IV (2005), pp. 63-72.
• A. Chertock and A. Kurganov, Conservative locally moving mesh method for multifluid flows, Finite Volumes for Complex Applications IV (2005), pp. 273-284.
• A. Chertock, A. Kurganov and P. Rosenau, On degenerate saturated-diffussion equations with convection, Nonlinearity, 18 (2005), pp. 609-630.
• A. Chertock and A. Kurganov, On a hybrid final-volume-particle method, Mathematical Modelling and Numerical Analysis, 38 (2004), pp. 1071–1091.
• A. Chertock and D. Levy, On wavelet-based numerical homogenization, SIAM Journal of Multiscale Modeling and Simulation, 3 (2004), pp. 65-88.
• A. Chertock, A. Kurganov and P. Rosenau, Formation of discontinuities in flux-saturated degenerate parabolic equations, Nonlinearity 16 (2003), pp. 1875-1898.
• A. Chertock and D. Levy, A particle method for the KdV equation, Journal of Scientific Computing, 17 (2002), pp. 491-499.
• A. Chertock, On the stability of a class of self-similar solutions for the filtration-absorption equation, European Journal of Applied Mathematics, 13 (2002), pp. 179-194.
• A. Chertock and D. Levy, Particle methods for dispersive equations, Journal of Computational Physics, 171 (2001), pp. 708-730.
• G.I. Barenblatt, M. Bertsch, A. Chertock and V.M. Prostokishin, Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation, Proceedings of National Academy of Sciences, USA, 97 (2000), pp. 9844-9848.
• S. Abarbanel, A Chertock and A. Yefet, Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, II, Journal of Computational Physics, 160 (2000), pp. 67-87.
• S. Abarbanel and A. Chertock, Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, I, Journal of Computational Physics, 160 (2000), pp. 42-66.
• A. Chertock, Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, PhD Thesis, Tel-Aviv University, Tel-Aviv, Israel ,1999.
• Yu. N. Karamzin, V. A. Trofimov and Chertok, A. E., An algorithm for the numerical solution of equations describing processes in photoreceivers. Journal of Mathematical Modeling, 3 (1991), pp. 95-103 (in Russian).