For the investigation of the high efficiency and high lift force of insect fight, a simulation of fluid field with a single wing at low Re is performed. The immersed boundary
method (IBM) is used to solve the complex flow with dynamically moving boundaries on fixed Cartesian grids. In comparison to the solutions of Wang [33] and Luo [35], the simulation results of IBM, such as vorticity field, CL and
CD, are quite accurate. To explore more details about the unsteady aerodynamics, several parameters investigated here include of path, stroke amplitude, Reynolds number (Re) and aspect ratio. The dierent paths correlate with the vortex shedding and the way of wake capture, and in this study, the horizontal stroke plane case shows a larger CL and CD. Based on the fraction of stroke amplitude and the chord length,
a larger amplitude means a larger flapping velocity, and results in a larger CL and CD. In the range of low Re, the profiles are almost the same but become greater on CL and smaller on CD as the Re increases. In the case of dierent aspect ratio(AR), it seems that after AR > 4, this characteristic does have a small contribution to CL and CD where CL is proportional to AR but CD is the opposite. For a further discussion of the dierent physical eects on the CL and CD, we introduce the force element theory. This theory isolates four constitute mechanisms, which all need surface integral on the immersed boundary. By assuming a linear relation in the vicinity of the boundary, we can do a linear interpolation to solve the coefficients, and finally get the desired variables. The interpolation stencil is eithered
isoscales-triangle or right-triangle based on the direction of normal vector (n) on the immersed-boundary.The results basically coincide with IBM, but the magnitude still needs continued modification.

For the investigation of the high efficiency and high lift force of insect fight, a simulation of fluid field with a single wing at low Re is performed. The immersed boundary
method (IBM) is used to solve the complex flow with dynamically moving boundaries on fixed Cartesian grids. In comparison to the solutions of Wang [33] and Luo [35], the simulation results of IBM, such as vorticity field, CL and
CD, are quite accurate. To explore more details about the unsteady aerodynamics, several parameters investigated here include of path, stroke amplitude, Reynolds number (Re) and aspect ratio. The dierent paths correlate with the vortex shedding and the way of wake capture, and in this study, the horizontal stroke plane case shows a larger CL and CD. Based on the fraction of stroke amplitude and the chord length,
a larger amplitude means a larger flapping velocity, and results in a larger CL and CD. In the range of low Re, the profiles are almost the same but become greater on CL and smaller on CD as the Re increases. In the case of dierent aspect ratio(AR), it seems that after AR > 4, this characteristic does have a small contribution to CL and CD where CL is proportional to AR but CD is the opposite. For a further discussion of the dierent physical eects on the CL and CD, we introduce the force element theory. This theory isolates four constitute mechanisms, which all need surface integral on the immersed boundary. By assuming a linear relation in the vicinity of the boundary, we can do a linear interpolation to solve the coefficients, and finally get the desired variables. The interpolation stencil is eithered
isoscales-triangle or right-triangle based on the direction of normal vector (n) on the immersed-boundary.The results basically coincide with IBM, but the magnitude still needs continued modification.

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