In the Lattice Boltzmann Method (LBM) the viscosity is inversely proportional to the relaxation frequency. Hence, it should be possible to represent the singularity of some viscoplastic models by setting the relaxation frequency to zero. In the present paper we take full advantage of the LBM capabilities to propose an efficient and stable numerical scheme for viscoplastic fluid flow simulations invoking the exact Bingham constitutive equation. This scheme is expected to suit the need for more accurate viscoplastic simulations because it does compute the “infinite viscosity”, therefore dismissing the need for any viscosity regularization. Although allowing for a wide range of relaxation frequencies varying in space and time, we demonstrate that the present implementation does not degrade the standard LBM's error order. Numerical stability was promoted by of regularization of ghost moments for the lattice Boltzmann equation with force term. Since the locality of the LBM is preserved, so is the scheme's ability to be highly scalable in large computer clusters. We outline the method and the theory behind it through a detailed Chapman–Enskog expansion. Three laminar test cases are analyzed: parallel channel Poiseuille flow, square duct Poiseuille flow and lid-driven cavity flow. We show conformity with the standard LBM's error order for different wall boundary conditions and yield stress levels. Comparisons are made with other numerical studies employing augmented Lagrangian and viscosity regularization methods.

在格子玻尔兹曼方法（LBM）中，粘度与松弛频率成反比。因此，应该可以通过将松弛频率设置为零来表示某些粘塑性模型的奇异性。在本文中，我们充分利用LBM的功能，为调用精确Bingham本构方程的粘塑性流体流动提出了一种有效且稳定的数值方案。由于该方案可以计算“无限粘度”，因此有望满足更精确的粘塑性模拟的需求，因此无需进行任何粘度正则化。尽管允许在空间和时间上变化的弛豫频率范围很广，但我们证明了本实现方式不会降低标准LBM的错误顺序。通过用力项对晶格Boltzmann方程进行幻影矩正则化，可以提高数值稳定性。由于保留了LBM的局部性，因此该方案在大型计算机群集中具有高度可伸缩性的能力也得到了保留。我们通过详细的Chapman–Enskog扩展概述了该方法及其背后的理论。分析了三个层流测试案例：平行通道泊瓦流，方管泊瓦流和盖驱动腔流。对于不同的壁边界条件和屈服应力水平，我们显示出符合标准LBM的误差顺序。与采用增强拉格朗日法和粘度正则化方法的其他数值研究进行了比较。该方案在大型计算机集群中具有高度可扩展性的能力也是如此。我们通过详细的Chapman–Enskog扩展概述了该方法及其背后的理论。分析了三个层流测试案例：平行通道泊瓦流，方管泊瓦流和盖驱动腔流。对于不同的壁边界条件和屈服应力水平，我们显示出符合标准LBM的误差顺序。与采用增强拉格朗日法和粘度正则化方法的其他数值研究进行了比较。该方案在大型计算机集群中具有高度可扩展性的能力也是如此。我们通过详细的Chapman–Enskog扩展概述了该方法及其背后的理论。分析了三个层流测试案例：平行通道泊瓦流，方管泊瓦流和盖驱动腔流。对于不同的壁边界条件和屈服应力水平，我们显示出符合标准LBM的误差顺序。与采用增强拉格朗日法和粘度正则化方法的其他数值研究进行了比较。对于不同的壁边界条件和屈服应力水平，我们显示出符合标准LBM的误差顺序。与采用增强拉格朗日法和粘度正则化方法的其他数值研究进行了比较。对于不同的壁边界条件和屈服应力水平，我们显示出符合标准LBM的误差顺序。与采用增强拉格朗日法和粘度正则化方法的其他数值研究进行了比较。