van Hinsberg M A T, Boonkkamp J H M ten Thije, Toschi F, Clercx H J H
Department of Physics, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):043307. doi: 10.1103/PhysRevE.87.043307. Epub 2013 Apr 15.
An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow field needed for the computation of the Lagrangian trajectories. The accuracy of the interpolation method has direct consequences for the acceleration spectrum of the fluid particles and is therefore also important for the correct evaluation of the hydrodynamic forces for almost neutrally buoyant particles, common in many environmental applications. In order to systematically choose the optimal tradeoff between interpolation accuracy and computational cost we focus on comparing errors: the interpolation error is compared with the discretization error of the flow field. In this way one can prevent unnecessary computations and still retain the accuracy of the turbulent flow simulation. From the analysis a practical method is proposed that enables direct estimation of the interpolation and discretization error from the energy spectrum. The theory is validated by means of direct numerical simulations (DNS) of homogeneous, isotropic turbulence using a spectral code, where the trajectories of fluid tracers are computed using several interpolation methods. We show that B-spline interpolation has the best accuracy given the computational cost. Finally, the optimal interpolation order for the different methods is shown as a function of the resolution of the DNS simulation.
含颗粒湍流流动数值模拟中的一个重要方面是计算拉格朗日轨迹所需的流场插值。插值方法的精度对流体颗粒的加速度谱有直接影响，因此对于正确评估许多环境应用中常见的几乎中性浮力颗粒的流体动力也很重要。为了系统地在插值精度和计算成本之间选择最佳权衡，我们专注于比较误差：将插值误差与流场的离散化误差进行比较。通过这种方式，可以避免不必要的计算，同时仍保持湍流模拟的精度。通过分析，提出了一种实用方法，该方法能够根据能谱直接估计插值误差和离散化误差。通过使用谱代码对均匀各向同性湍流进行直接数值模拟（DNS）验证了该理论，其中使用几种插值方法计算流体示踪剂的轨迹。我们表明，在给定计算成本的情况下，B样条插值具有最佳精度。最后，给出了不同方法的最佳插值阶数与DNS模拟分辨率的函数关系。
