Advection of inertial particles in the presence of the history force: higher order numerical schemes. (English) Zbl 1349.65223
Summary: The equations describing the motion of finite-size particles (inertial particles) contain in their full form the history force. This force is represented by an integral whose accurate numerical evaluation is rather difficult. Here, a systematic way is presented to derive numerical integration schemes of arbitrary order for the advection of inertial particles with the history force. This involves the numerical evaluation of integrals with singular, but integrable, integrands. Explicit specifications of first, second and third order schemes are given and the accuracy and order of the schemes are verified using known analytical solutions.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 45J05 | Integro-ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
history force; inertial particles; numerical approximation; Maxey-Riley equation; fractional differential equation; singular integrandReferences:
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