An improved flux limiter using fuzzy modifiers for Hyperbolic Conservation Laws

Abstract

The objective of the work in this paper is to computationally tackle a range of problems in hyperbolic conservation laws, which is an interesting branch of computational fluid dynamics. For the simulation of issues in hyperbolic conservation laws, this work explores the concept of fuzzy logic-based operators. This research presents a unique mixture of fuzzy sets and logic with a new branch of conservation laws from fluid dynamics. The approach considers a computational procedure based on the reconstruction of several high-order numerical methods termed as flux-limited methods using some fuzzy logic operators. With the aid of fuzzy modifiers, these flux limiters are further modified. This approach results in improved convergence of approximations and maintains the problem’s basic properties to be solved. Additionally, to ensure improved results, modified flux-limited methods are imposed on some famous test problems. The application results are provided wherever required. The work has demonstrated that it is possible to use such technique and apply it to complex areas of computational fluid dynamics to produce a more straightforward approach to studying other topics like flux-limited methods and hence opens up an exciting gateway for future work.