ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations
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Publication:554669
DOI10.1007/s10915-010-9426-6zbMath1221.65231OpenAlexW2095572773MaRDI QIDQ554669
Michael Dumbser, Arturo Hidalgo
Publication date: 4 August 2011
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-010-9426-6
stiff source termsADER approachadvection-diffusion-reaction equationsasymptotic preserving propertycompressible Navier-Stokes equations with chemical reactionshigh order finite volume schemes
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Arbitrary high order \(P_{N}P_{M}\) schemes on unstructured meshes for the compressible Navier-Stokes equations
- A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems
- FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems
- Very high order \(P_NP_M\) schemes on unstructured meshes for the resistive relativistic MHD equations
- A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
- ADER finite volume schemes for nonlinear reaction-diffusion equations
- Uniformly high order accurate essentially non-oscillatory schemes. III
- High accuracy numerical methods for thermally perfect gas flows with chemistry
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- Numerical approximation of hyperbolic systems of conservation laws
- Efficient implementation of weighted ENO schemes
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
- A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
- High-Order Unstructured One-Step PNPM Schemes for the Viscous and Resistive MHD Equations
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations