A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis
From MaRDI portal
Publication:292559
DOI10.1007/s10915-015-0097-1zbMath1350.65093OpenAlexW2117424537MaRDI QIDQ292559
Christophe Berthon, Anaïs Crestetto, Françoise Foucher
Publication date: 8 June 2016
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-015-0097-1
finite volume methodRiemann solvernumerical resultchemotaxis modelasymptotic preserving schemesfinite volume method of Godunov typemixed hyperbolic/parabolic PDEwell-balanced schemes
Nonlinear parabolic equations (35K55) Classical flows, reactions, etc. in chemistry (92E20) First-order nonlinear hyperbolic equations (35L60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Mixed-type systems of PDEs (35M30)
Related Items (6)
A well-balanced scheme for the shallow-water equations with topography or Manning friction ⋮ Unnamed Item ⋮ A novel growing wavelet neural network algorithm for solving chemotaxis systems with blow‐up ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ A well-balanced scheme for the shallow-water equations with topography ⋮ Well-balancing via flux globalization: applications to shallow water equations with wet/dry fronts
Uses Software
Cites Work
- Unnamed Item
- Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
- Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
- A simple well-balanced and positive numerical scheme for the shallow-water system
- A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime
- Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes
- A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations
- A second-order Godunov-type scheme for compressible fluid dynamics
- A direct Eulerian GRP scheme for compressible fluid flows
- Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions
- A multiwave approximate Riemann solver for ideal MHD based on relaxation. II: Numerical implementation with 3 and 5 waves
- The Boltzmann equation and its applications
- Restoration of the contact surface in the HLL-Riemann solver
- Positive and entropy-stable Godunov-type schemes for gas dynamics and MHD equations in Lagrangian or Eulerian coordinates
- A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
- An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations
- Entropic Godunov-type schemes for hyperbolic systems with source term
- Well-balanced schemes for the shallow water equations with Coriolis forces
- A well-balanced positivity preserving ``second-order scheme for shallow water flows on unstructured meshes
- Numerical approximation of hyperbolic systems of conservation laws
- Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation
- A well-balanced numerical scheme for a one-dimensional quasilinear hyperbolic model of chemotaxis
- Stability of constant states and qualitative behavior of solutions to a one dimensional hyperbolic model of chemotaxis
- A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis
- Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem
- High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
- Upwinding of the source term at interfaces for Euler equations with high friction
- An asymptotic preserving scheme for hydrodynamics radiative transfer models. Numerics for radiative transfer
- An HLLC scheme to solve the \(M_{1}\) model of radiative transfer in two space dimensions
- Asymptotic preserving and positive schemes for radiation hydrodynamics
- A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
- A steady-state capturing method for hyperbolic systems with geometrical source terms
- Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
- Analysis of an Asymptotic Preserving Scheme for Relaxation Systems
- Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms
- Maxwellian Decay for Well-balanced Approximations of a Super-characteristic Chemotaxis Model
- Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis
- GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION
- Asymptotic preserving HLL schemes
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- Numerical Approximations of Pressureless and Isothermal Gas Dynamics
- Space Localization and Well-Balanced Schemes for Discrete Kinetic Models in Diffusive Regimes
- Finite Volume Methods for Hyperbolic Problems
- A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
- Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
- Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness
- A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
- Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations
- A relaxation scheme for the approximation of the pressureless Euler equations
- Approximation of Hyperbolic Models for Chemosensitive Movement
- A class of approximate Riemann solvers and their relation to relaxation schemes
This page was built for publication: A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis
