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Effects of Truncation Error of Derivative Approximation for Two-Phase Lattice Boltzmann Method

机译：两相晶格Boltzmann方法的衍生近似截断误差的影响

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摘要

We verify the accuracy and the truncation errors of approximation to the first derivatives and to Laplacian operator in the lattice Boltzmann method. The truncation errors are calculated by the Taylor series expansion, and the influences are analytically and numerically examined in the simulation of two-phase flow. We propose the 4th-order accurate approximations to derivatives that utilize the property of the tensor unlike the finite difference. Application of the 4thorder accurate approximation scheme to two-phase flow simulation reduces the spurious current around the interface of a stationary droplet about to one-half of the results with the 2nd-order accuracy. The small spurious velocity in the vicinity of the interface of the 4th-order approximation increases the speed of a moving droplet, and distorts the shape of the droplet little. It is shown that the approximation method affects the important physical values, such as velocity, moving speed, or domain size in numerical simulations.
机译：我们验证了近似值的准确性和截断误差，以及在晶格Boltzmann方法中的拉普拉斯操作员。截断误差由泰勒序列扩展计算，在模拟两相流的模拟中分析和数值检查的影响。我们提出了与有限差异不同于张量的衍生品的第4次准确的近似。将4个精确近似方案应用于两相流模拟，减少了静止液滴界面周围的虚假电流，其次具有2nd阶精度的结果的一半。第四阶近似界面附近的小奇迹速度增加了移动液滴的速度，并扭曲了液滴的形状。结果表明，近似方法影响数值模拟中的重要物理值，例如速度，移动速度或域大小。

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