A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is explored and bounds derived for such limiters. A class of limiters is presented which includes a very compressive limiter due to Roe, and various limiters are compared both theoretically and numerically.

Fuzzy flux limiter schemes for hyperbolic conservation laws

A classic strategy to obtain high-quality discretisations of hyperbolic partial differential equations (PDEs) is to employ a non-linear mixture of two types of approximations. The building blocks for this are a monotone first-order scheme that deals with discontinuous solution features and a higher-order method for approximating the smooth solution parts. The blending is performed by the so-cal...

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two nei...

A Finite Element, Multiresolution Viscosity Method for Hyperbolic Conservation Laws

It is well known that the classic Galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the Euler equations for compressible flow. It is also well known that naively adding artificial diffusion to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use. An elegant approach, referred to as spectral viscosity method...