Multidimensional finite-element particle tracking method for solving complex transient flow problems

This paper proposes a particle tracking technique for applying the Eulerian-Lagrangian localized adjoint method or the Eulerian-Lagrangian method to solve transport equations in a rapidly changing unsteady flow. The proposed particle tracking technique uses a linear temporal interpolation of velocity to avoid the error introduced when using a stepwise temporal approximation of the velocity, which has been adopted in many existing particle tracking techniques. Numerical experiments were carried out on several example problems to demonstrate the superior accuracy and efficiency of the proposed particle tracking technique over Cheng's and Pollock's methods. The numerical results show that the use of a linear temporal interpolation of velocity can allow an increase in time step size without causing a significant decrease in accuracy, particularly under a complicated transient flow or a rapidly changing velocity field with time.