Numerical Simulation of Hyperbolic Conservation Laws Using High Resolution Schemes with the Indulgence of Fuzzy Logic

  • Ruchika Lochab
  • Vivek KumarEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11974)


The aim of this paper is to solve numerically a class of problems on conservation laws, modelled by hyperbolic partial differential equations. In this paper, primary focus is over the idea of fuzzy logic-based operators for the simulation of problems related to hyperbolic conservation laws. Present approach considers a novel computational procedure which relies on using some operators from fuzzy logic to reconstruct several higher-order numerical methods known as the flux-limited methods. Further optimization of the flux limiters is discussed. The approach ensures better convergence of the approximation and preserves the basic properties of the solution of the problem under consideration. The new limiters are further applied to several real-life problems like the advection problem to demonstrate that the optimized schemes ensure better results. Simulation results are included wherever required.


Conservation laws Flux limiters Fuzzy logic 



RL thanks the Delhi Technological University for the partial financial support to attend NUMTA 2019 and UGC for PhD fellowship.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Applied MathematicsDelhi Technological UniversityDelhiIndia

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