A new TVD flux-limiter method for solving nonlinear hyperbolic equations

DOI10.1016/J.CAM.2010.02.015zbMath1205.65234OpenAlexW1976692802MaRDI QIDQ972744

Silvia Jerez Galiano, Miguel Uh Zapata

Publication date: 21 May 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.02.015

zbMATH Keywords

stabilityconservation lawsBurgers equationhyperbolic equationsBuckey-Leverett equationflux-limiter schemesnonlinear advection equationRichtmyer two-step Lax-Wendroff methodtotal-variation diminishing (TVD)

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Hyperbolic conservation laws (35L65) 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 (5)

Switch flux limiter method for viscous and nonviscous conservation laws ⋮ A flux-limiter method for modeling blood flow in the aorta artery ⋮ A high resolution nonstandard FDTD method for the TM mode of Maxwell's equations ⋮ Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning ⋮ Monotone first-order weighted schemes for scalar conservation laws

Uses Software

• GFORCE
• SHASTA

Cites Work

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• High resolution schemes for hyperbolic conservation laws. (Reprint)
• A semi-implicit space-time CE-SE method to improve mass conservation through tapered ducts in internal combustion engines
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• MUSTA fluxes for systems of conservation laws
• Analysis of numerical methods to solve one-dimensional fluid-dynamic governing equations under impulsive flow in tapered ducts
• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• Computational Gasdynamics
• Composite Schemes for Conservation Laws
• Convergence of difference schemes with high resolution for conservation laws
• Finite Volume Methods for Hyperbolic Problems
• Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works

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