We present a meshfree computational framework for incompressible Bingham flows based on radial basis function-generated finite differences (RBF-FD) combined with an augmented Lagrangian (ALM) formulation enforcing the viscoplastic constraint. A Uzawa-type splitting strategy decouples updates of velocity, pressure, and an auxiliary deformation field, yielding a structured velocity–pressure system assembled directly within the RBF-FD discretization.

The main contributions are: (i) a cost-effective ALM-RBF-FD scheme for viscoplastic flows on collocated nodes, (ii) a mixed-order polynomial augmentation strategy that improves enforcement of incompressibility, and (iii) a numerical study of sensitivity associated with constitutive non-smoothness at high Bingham numbers.

The formulation is assessed across a range of Bingham numbers with emphasis on flow structure, yield-surface localization, and iterative behavior. For moderate Bingham numbers, the method accurately captures plug formation and shear localization while achieving substantially lower computational cost than comparable finite element discretizations, demonstrating the efficiency of meshfree RBF-FD methods for viscoplastic flow simulation.

At higher Bingham numbers, sensitivity increases near yield-transition regions, producing oscillatory behavior in constitutive fields and reduced smoothness in the velocity solution. These effects are attributed to limited regularity of the constitutive response together with amplification mechanisms inherent in meshfree differentiation. To mitigate these difficulties, mixed-order polynomial augmentation and localized smoothing within the ALM iteration are examined as preliminary stabilization mechanisms.

Future work will focus on improving robustness in strongly yield-dominated regimes through adaptive stabilization guided by local flow indicators and improved consistency between constitutive updates and meshfree discretization operators.