Volume 26, Issue 3
An Adaptive High Order WENO Solver for Conservation Laws

Cheng Liu & Changhong Hu

Commun. Comput. Phys., 26 (2019), pp. 719-748.

Published online: 2019-04

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  • Abstract

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 hybridWENO 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 lowdissipative 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

  • Keywords

Block-structured AMR, WENO, Euler equations, Navier-Stokes equations, large scale computation.

  • AMS Subject Headings

76L05, 76F65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-719, author = {}, title = {An Adaptive High Order WENO Solver for Conservation Laws}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {3}, pages = {719--748}, abstract = {

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 hybridWENO 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 lowdissipative 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

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0059}, url = {http://global-sci.org/intro/article_detail/cicp/13144.html} }
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