The shock-fitting method embeds the analytical relationship into the flow field to avoid the theoretical problems caused by discontinuity, making it possible to achieve consistent high order scheme in the whole flow field. It is expected to solve the susceptibility simulation problem in the research of supersonic flow transition. However, after complex shock wave structures are fitted, the segmented flow field space often has irregular geometric shapes, bringing difficulties to the conventional finite difference method based on structural mesh. In this paper, based on the theory of discrete equivalence equations, a new finite difference method for unstructured mesh is proposed. In the case of two-dimensional space, a first-order upwind scheme can be constructed by only using three mesh lines at discrete points. Numerical examples show that the convergence process is not sensitive to the quality of the mesh. The proposed scheme is used in the shock-fitting simulation to solve the problem that the structural mesh appears after the shock wave intersects with a small angle. Finally, this paper forecasts the application prospects of the proposed scheme according to its characteristics.
LIU Jun
,
CHEN Jie
,
HAN Fang
. Finite difference method for unstructured grid based on discrete equivalent equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(1)
: 123248
-123248
.
DOI: 10.7527/S1000-6893.2019.23248
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