Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A finite volume scheme for the Patlak–Keller–Segel chemotaxis model
Numerische Mathematik
Journal of Computational Physics
Discontinuous Galerkin methods for the chemotaxis and haptotaxis models
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model
SIAM Journal on Numerical Analysis
Monoslope and multislope MUSCL methods for unstructured meshes
Journal of Computational Physics
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We develop a novel upwind-difference potentials method for the Patlak-Keller-Segel chemotaxis model that can be used to approximate problems in complex geometries. The chemotaxis model under consideration is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration.Chemotaxis is an important process in many medical and biological applications, including bacteria/cell aggregation and pattern formation mechanisms, as well as tumor growth. Furthermore modeling of real biomedical problems often has to deal with the complex structure of computational domains. There is consequently a need for accurate, fast, and computationally efficient numerical methods for different chemotaxis models that can handle arbitrary geometries.The upwind-difference potentials method proposed here handles complex domains with the use of only Cartesian meshes, and can be easily combined with fast Poisson solvers. In the numerical tests presented below we demonstrate the robustness of the proposed scheme.