Higher-Order Slope Limiters for Euler Equation

High-resolution schemes are designed for resolving shocks without significant numerical dissipation and dispersion. Achieving higher-order and high-resolution is a challenging task because of the non-monotonicity of the higher-order schemes. In this article, we have presented second-order and third-order slope limiters having an improved shock resolution and accuracy. The present limiters are tested on one-dimensional and two-dimensional unstructured grids and compared with the existing limiters. The numerical result shows that the present limiters have an excellent shock resolving property and accuracy than other limiters. In blast wave problems, it has shown over ۲۰۰% more accurate results than the other limiters.

Keywords:

Finite volume method , high-resolution method , higher-order methods , slope-limiter