A high-order Godunov method for one-dimensional convection-diffusion-reaction problems

DOI<495::AID-NUM1>3.0.CO;2-S 10.1002/1098-2426(200011)16:6<495::AID-NUM1>3.0.CO;2-SzbMath0967.65093OpenAlexW2050839686MaRDI QIDQ4521943

Junping Wang, Shaochang Wo, Benito M. Chen

Publication date: 21 August 2001

Full work available at URL: https://doi.org/10.1002/1098-2426(200011)16:6<495::aid-num1>3.0.co;2-s

zbMATH Keywords

Godunov methodMUSCL schemecomputational examplesconvection-diffusion-reaction equationsmonotonicity preservationtotal variation stability

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (1)

New characteristic difference method with adaptive mesh for one-dimensional unsteady convection-dominated diffusion equations

Cites Work

• The piecewise parabolic method (PPM) for gas-dynamical simulations
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• An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Some Improved Error Estimates for the Modified Method of Characteristics
• A Direct Eulerian MUSCL Scheme for Gas Dynamics
• Riemann Solvers, the Entropy Condition, and Difference
• The Scalar Riemann Problem in Two Spatial Dimensions: Piecewise Smoothness of Solutions and Its Breakdown
• Convergence of Generalized MUSCL Schemes
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Godunov-Mixed Methods for Advective Flow Problems in One Space Dimension
• A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems
• A modified method of characteristics incorporating streamline diffusion
• High resolution upwind‐mixed finite element methods for advection‐diffusion equations with variable time‐stepping

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