The equations describing the motion of finite-size particles (inertialparticles) contain in their full form the history force. This force isrepresented by an integral whose accurate numerical evaluation is ratherdifficult. Here, a systematic way is presented to derive numerical integrationschemes of arbitrary order for the advection of inertial particles with thehistory force. This involves the numerical evaluation of integrals withsingular, but integrable, integrands. Explicit specifications of first, secondand third order schemes are given and the accuracy and order of the schemes areverified using known analytical solutions.
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