Displaying similar documents to “The correct use of the Lax–Friedrichs method”

A steady-state capturing method for hyperbolic systems with geometrical source terms

Shi Jin (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments...

An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws

Michael Breuss (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov’s method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov’s method....

Genuinely multi-dimensional non-dissipative finite-volume schemes for transport

Bruno Després, Frédéric Lagoutière (2007)

International Journal of Applied Mathematics and Computer Science

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We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière,...