Numerical viscosity and the entropy condition for conservative difference schemes

1984/01/01 by Eitan Tadmor · 6 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Advanced Mathematical Physics Problems #Differential Equations and Numerical Methods

paper · pdf · doi:10.1090/s0025-5718-1984-0758189-x

Abstract

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing <italic>more</italic> numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservative equation. In particular, entropy satisfying convergence follows for <italic>E</italic> schemes—those containing more numerical viscosity than Godunov’s scheme.

Citations

• Symmetric hyperbolic linear differential equations

Cited by

• The numerical viscosity of entropy stable schemes for systems of conservation laws. I
• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• An Analysis of the Riemann Problem for a 2 × 2 System of Keyfitz-Kranzer Type Balance Laws With a Time-Dependent Source Term
• An Analysis of the Riemann Problem for a 2 × 2 System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization
• Recent results on the singular local limit for nonlocal conservation laws
• On the role of numerical viscosity in the study of the local limit of\n nonlocal conservation laws

Related

• The numerical viscosity of entropy stable schemes for systems of conservation laws. I
• Entropy stable finite difference methods via entropy correction artificial viscosity and knapsack limiting
• On the scaling of entropy viscosity in high order methods
• Analysis of an alternative Navier-Stokes system: Weak entropy solutions and a convergent numerical scheme
• Stability theory for difference approximations of some dispersive\n shallow water equations and application to thin film flows