ADER finite volume schemes for nonlinear reaction-diffusion equations
From MaRDI portal
Publication:960290
DOI10.1016/j.apnum.2007.12.001zbMath1155.65065OpenAlexW2094184168MaRDI QIDQ960290
Arturo Hidalgo, Eleuterio F. Toro
Publication date: 16 December 2008
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2007.12.001
ADERCauchy problemnumerical examplessource termshigh-order methodsnonlinear reaction-diffusion equationsfinite volumesGodunov's methodarbitrary accuracyderivative Riemann problem
Related Items (27)
Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials ⋮ A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension ⋮ An ADER-LSTDG Scheme for the Numerical Simulation of a Global Climate Model ⋮ Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws ⋮ Multi-dimensional Optimal Order Detection (MOOD) — a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured Meshes ⋮ High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids ⋮ A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws ⋮ Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes ⋮ Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations ⋮ Riemann problem for constant flow with single-point heating source ⋮ Numerical approach of a coupled pressure-saturation model describing oil-water flow in porous media ⋮ Arbitrary high order \(P_{N}P_{M}\) schemes on unstructured meshes for the compressible Navier-Stokes equations ⋮ A new mean preserving moving least squares method for arbitrary order finite volume schemes ⋮ A sixth-order finite volume method for multidomain convection-diffusion problem with discontinuous coefficients ⋮ On a climatological energy balance model with continents distribution ⋮ A very high-order finite volume method based on weighted least squares for elliptic operators on polyhedral unstructured grids ⋮ Improved accuracy for time-splitting methods for the numerical solution of parabolic equations ⋮ Numerical and analytical study of an atherosclerosis inflammatory disease model ⋮ Uniformly high-order schemes on arbitrary unstructured meshes for advection-diffusion equations ⋮ An efficient implicit spectral element method for time-dependent nonlinear diffusion equations by evaluating integrals at one quadrature point ⋮ Heat and mass transfer in unsaturated porous media: moisture effects in compost piles self-heating ⋮ ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations ⋮ Numerical simulation of a porous medium-type atherosclerosis initiation model ⋮ HFVS: an arbitrary high order approach based on flux vector splitting ⋮ A sixth-order finite volume method for diffusion problem with curved boundaries ⋮ A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation ⋮ A numerical scheme for a partial differential system motivated by light-triggered drug delivery
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local discontinuous Galerkin methods for nonlinear dispersive equations
- On WAF-type schemes for multidimensional hyperbolic conservation laws
- The piecewise parabolic method (PPM) for gas-dynamical simulations
- A second-order Godunov-type scheme for compressible fluid dynamics
- A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes
- Solution of the porous media equation by Adomian's decomposition method
- Uniformly high order accurate essentially non-oscillatory schemes. III
- Asymptotic behaviour for the porous medium equation posed in the whole space.
- ADER: Arbitrary high-order Godunov approach
- Axisymmetric vortex method for low-Mach number, diffusion-controlled combustion.
- Finite speed of propagation in porous media by mass transportation methods
- The finite volume method for Richards equation
- Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
- Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
- Derivative Riemann solvers for systems of conservation laws and ader methods
- A weighted average flux method for hyperbolic conservation laws
- An Interior Penalty Finite Element Method with Discontinuous Elements
- Asymptotic Behavior of Solutions of a Nonlinear Diffusion Equation
- Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
- Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
- A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media
- Solution of the generalized Riemann problem for advection–reaction equations
- Finite Volume Methods for Hyperbolic Problems
- Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
- A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media
- Analysis of ADER and ADER-WAF schemes
- Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing
- Modeling evaporation using a nonlinear diffusion equation
This page was built for publication: ADER finite volume schemes for nonlinear reaction-diffusion equations