In this paper, a novel semi-implicit lubrication dynamics method that can efficiently simulate dense non-colloidal suspensions is proposed. To reduce the computational cost in the presented methodology, inter-particle lubrication-based forces and torques alone are considered together with a short-range repulsion to enforce finite inter-particle separation due to surface roughness, Brownian forces or other excluded volume effects. Given that the lubrication forces are singular, i.e. scaling inversely with the inter-particle gap, the strategy to expedite the calculations is severely compromised if explicit integration schemes are used, especially at high concentrations. To overcome this issue, an efficient semi-implicit splitting integration scheme to solve for the particles translational and rotational velocities is presented. To validate the proposed methodology, a suspension under simple shear test is simulated in three dimensions and its rheology is compared against benchmark results. To demonstrate the stability/speed-up in the calculations, performance of the proposed semi-implicit scheme is compared against a classical explicit Velocity-Verlet scheme. The predicted viscometric functions for a non-colloidal suspension with a Newtonian matrix are in excellent agreement with the reference data from the literature. Moreover, the presented semi-implicit algorithm is found to be significantly faster than the classical lubrication dynamics methods with Velocity-Verlet integration schemes.

本文提出了一种新的半隐式润滑动力学方法，可以有效地模拟稠密的非胶体悬浮液。为了减少所提出方法中的计算成本，仅考虑基于颗粒间润滑的力和扭矩以及短程斥力，以由于表面粗糙度，布朗力或其他排除的体积效应而强制进行有限的颗粒间分离。考虑到润滑力是奇异的，即与颗粒间的间隙成反比，如果使用显式积分方案（尤其是在高浓度下），则加速计算的策略将受到严重损害。为了克服这个问题，提出了一种有效的半隐式分裂积分方案，以解决粒子的平移和旋转速度。为了验证所提出的方法，在三个方向上模拟了简单剪切试验下的悬浮液，并将其流变性与基准结果进行了比较。为了证明计算的稳定性/提速性，将所提出的半隐式方案的性能与经典的显式Velocity-Verlet方案进行了比较。具有牛顿矩阵的非胶体悬浮液的预测粘度函数与文献中的参考数据非常吻合。此外，发现提出的半隐式算法比采用Velocity-Verlet积分方案的经典润滑动力学方法要快得多。为了证明计算的稳定性/提速性，将所提出的半隐式方案的性能与经典的显式Velocity-Verlet方案进行了比较。具有牛顿矩阵的非胶体悬浮液的预测粘度函数与文献中的参考数据非常吻合。此外，发现提出的半隐式算法比采用Velocity-Verlet积分方案的经典润滑动力学方法要快得多。为了证明计算的稳定性/提速性，将所提出的半隐式方案的性能与经典的显式Velocity-Verlet方案进行了比较。具有牛顿矩阵的非胶体悬浮液的预测粘度函数与文献中的参考数据非常吻合。此外，发现提出的半隐式算法比采用Velocity-Verlet积分方案的经典润滑动力学方法要快得多。