Development of higher-order accurate spatial interpolation scheme for unstructured cartesian grids

Yoshiharu Tamaki, Taro Imamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution


New higher-order accurate spatial interpolation schemes for the finite-volume method (FVM) on unstructured Cartesian grids are proposed. In the FVM formulation, the accuracy of both the interpolation of the variable and the flux quadrature affects the formal spatial accuracy. In this paper, the accuracy of the interpolation using the gradients of the variable is considered. The gradient is conventionally approximated using Green-Gauss method or weighted least-square method, but the accuracy is less than second-order; therefore, the gradient is reformulated using the gradient values saved in the adjacent cells. This corresponds to virtually extending the stencils, and fifth-order accuracy is achieved with referring to only the adjacent cells. This formulation is based on the advantage of Cartesian grids, i.e. the most part of the grid is uniform. In the twodimensional problem, the present schemes show better preservability of an isentropic vortex. Finally, a two-dimensional direct acoustic simulation is conducted. The result shows that the present schemes have better wave resolution, and is consistent with the result using conventional third-order scheme on finer grids. It is also confirmed that the present scheme has enough stability in the problem. The present schemes have good balance between the resolution and the computational cost compared with the conventional higher-order schemes for unstructured grids.

Original languageEnglish
Title of host publication20th AIAA/CEAS Aeroacoustics Conference
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781624102851
Publication statusPublished - 2014
Externally publishedYes
Event20th AIAA/CEAS Aeroacoustics Conference 2014 - Atlanta, GA, United States
Duration: 2014 Jun 162014 Jun 20

Publication series

Name20th AIAA/CEAS Aeroacoustics Conference


Conference20th AIAA/CEAS Aeroacoustics Conference 2014
Country/TerritoryUnited States
CityAtlanta, GA

ASJC Scopus subject areas

  • Aerospace Engineering
  • Mechanical Engineering


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