An adaptive high order WENO solver for conservation laws

Cheng Liu, Changhong Hu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper presents an implementation of the adaptive hybrid WENO (weighted essentially non-oscillatory) scheme based on our previous investigations for compressible multi-medium flows (Liu and Hu, J. Comput. Phys., 342 (2017), 43-65). In this study a simple and efficient method is developed for Euler equations and Navier-Stokes equations arising from the conservation laws. A class of high order weighted essentially non-oscillatory (WENO) schemes are applied to resolve the complicated flow structures and shock waves. Classical WENO schemes are computationally expensive in calculating the non-linear weight and smoothness indicators. We propose a block-structured adaptive mesh method together with a modified hybrid-WENO scheme to reduce the cost, the reconstruction is only performed at non-smooth region. Comparisons of WENO scheme with various smoothness indicators and different Lax-Friedrich flux vector splitting methods are performed on block structured adaptive mesh. Benchmark tests show present adaptive hybrid WENO method is low-dissipative and highly robust. The 2-D/3-D shock wave boundary layer interaction are simulated to verify the efficiency of present AMR (adaptive mesh refinement) solver in predicting turbulent flow.

Original languageEnglish
Pages (from-to)719-748
Number of pages30
JournalCommunications in Computational Physics
Issue number3
Publication statusPublished - Sept 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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