High order accurate shock capturing schemes for hyperbolic conservation laws based on a new class of limiters.

2005

We have introduced new shock capturing schemes that reduce the numerical diusion at discontinuities, sharpen the discontinuities in derivative and avoid spurious oscillations, improving the behavior of essentially non oscillatory schemes and piecewise hyperbolic methods. We have introduced and analyzed in this work a new class of limiter functions, the so called power limiters", which are an essential tool for the construction of these schemes. When power limiters are used as limiters of rst or second order dierences, the resulting methods behave essentially non-oscillatory near discontinuities and they allow simple expressions of the local truncation errors when they are used as limiters o…