A moving-mesh gradient smoothing method for compressible CFD problems

Jianyao Yao, G. R. Liu*, Dong Qian, Chung-Lung Chen, George X. Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


A computational fluid dynamics (CFD) solver based on the gradient smoothing method (GSM) with moving mesh enabled is presented in this paper. The GSM uses unstructured meshes which could be generated and remeshed easily. The spatial derivatives of field variables at nodes and midpoints of cell edges are calculated using the gradient smoothing operations. The presented GSM codes use second-order Roes upwind flux difference splitting method and second-order 3-level backward differencing scheme for the compressible Navier-Stokes equations with moving mesh, and the second-order of accuracy for both the spatial and temporal discretization is ensured. The spatial discretization accuracy is verified using the method of manufactured solutions (MMS) on both structured and unstructured triangle meshes, and the results show that the observed order of accuracy achieves 2 even when highly distorted meshes are used. The temporal discretization accuracy is verified using the results with different time step lengths, and second-order accuracy is also obtained. Therefore, it is confirmed that the proposed GSM-CFD solver is a uniform second-order scheme.

Original languageEnglish
Pages (from-to)273-305
Number of pages33
JournalMathematical Models and Methods in Applied Sciences
Issue number2
StatePublished - 1 Feb 2013


  • CFD
  • Gradient smoothing method (GSM)
  • Method of manufactured solutions (MMS)
  • Moving mesh
  • Verification

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