Generalized implementation of the order-preserving mapping for mapped WENO schemes

by   Ruo Li, et al.

A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions and in the meantime prevent spurious oscillations on solving hyperbolic conservation laws with long output times. Our goal in this article is to address this widely concerned problem [3,4,15,29,16,18].We firstly take a closer look at the mappings of various existing mapped WENO schemes and devise a general formula for them. It helps us to extend the order-preserving (OP) criterion, originally defined and carefully examined in [18], into the design of the mappings.Next, we propose the implementation of obtaining the new mappings satisfying the OP criterion from those of the existing mapped WENO-X schemes where the notation "X" is used to identify the version of the existing mapped WENO scheme, e.g., X = M [11], PM6 [3], or PPM5 [15], et al. Then we build the resultant mapped WENO schemes and denote them as MOP-WENO-X. The numerical solutions of the one-dimensional linear advection equation with different initial conditions and some standard numerical experiments of two-dimensional Euler system, computed by the MOP-WENO-X schemes, are compared with the ones generated by their corresponding WENO-X schemes and the WENO-JS scheme. To summarize, the MOP-WENO-X schemes gain definite advatages in terms of attaining high resolutions and meanwhile avoiding spurious oscillations near discontinuities for long output time simulations of the one-dimensional linear advection problems, as well as significantly reducing the post-shock oscillations in the simulations of the two-dimensional steady problems with strong shock waves.



There are no comments yet.


page 26


Locally Order-Preserving Mapping for WENO Methods

Most of the existing mapped WENO schemes suffer from either losing high ...

An extension of the order-preserving mapping to the WENO-Z-type schemes

In our latest studies, by introducing the novel order-preserving (OP) cr...

A new mapped WENO scheme using order-preserving mapping

Existing mapped WENO schemes can hardly prevent spurious oscillations wh...

On developing piecewise rational mapping with fine regulation capability for WENO schemes

On the idea of mapped WENO-JS scheme, properties of mapping methods are ...

A modified adaptive improved mapped WENO method

We propose several adaptive control functions and a smoothing approximat...

An efficient mapped WENO scheme using approximate constant mapping

We present a novel mapping approach for WENO schemes through the use of ...

Convergence analysis of some tent-based schemes for linear hyperbolic systems

Finite element methods for symmetric linear hyperbolic systems using uns...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.