Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows

  • Authors:

  • Kyu Hong Kim;Chongam Kim

  • Affiliations:

  • Department of Aerospace Engineering, School of Mechanical and Aerospace Engineering, Seoul National University, Kwanak-Gu, Shilim-Dong, Seoul 151-742, Republic of Korea;Department of Aerospace Engineering, School of Mechanical and Aerospace Engineering, Seoul National University, Kwanak-Gu, Shilim-Dong, Seoul 151-742, Republic of Korea

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

The present papers deal with numerical methods toward the accurate and efficient computations of multi-dimensional steady/unsteady compressible flows. In Part I, a new spatial discretization technique is introduced to reduce excessive numerical dissipation in a non-flow-aligned grid system. Through the analysis of TVD limiters, a criterion is proposed to predict cell-interface states accurately both in smooth region and in discontinuous region. According to the criterion, a new way of re-evaluating the cell-interface convective flux in AUSM-type methods is developed. The resultant flux reduces numerical dissipation remarkably in multi-dimensional flows. Also, the monotonicity of AUSM-type methods is achieved by modifying the pressure splitting function directly based on the governing equations and the detection of sonic transition point with respect to a cell-interface. It is noted that the newly formulated AUSM-type flux for Multi-dimensional flows, named M-AUSMPW+, possesses many improved properties in term of accuracy, computational efficiency, monotonicity and grid independency. Through numerous test cases from contact and shock discontinuities, vortex flow, shock wave/boundary-layer interaction to viscous shock tube problems, M-AUSMPW+ proves to be efficient and about twice more accurate than conventional upwind schemes. The three-dimensional implementation of M-AUSMPW+ is expected to provide accuracy and efficiency improvement furthermore.