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This paper presents a new method of semianalytical particle tracking analysis under transient conditions. To permit accurate particle tracking in transient flows, the particle velocity is interpolated linearly in both space and time coordinates within each finite difference cell and time step. By using the total derivative and this interpolation scheme, the particle velocity is derived and integrated analytically to obtain the particle's trajectory within each cell and time step. Errors are much smaller than in numerical integration schemes. Numerical experiments show that the transient semianalytical solutions are efficient and accurate.
Ning Lu (Mon,) studied this question.