An Implicit Lagrangian Generalized Finite Difference Method for Flow Problems

doi:10.1016/j.cpc.2026.110191

An Implicit Lagrangian Generalized Finite Difference Method for Flow Problems

2026-05-06

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DOI：10.1016/j.cpc.2026.110191

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Aiming to address the limitations of traditional explicit solution methods arising from time step constraints in the simulation of complex transient flows, this paper introduces a Lagrangian generalized finite difference method that integrates an implicit time integration scheme. The approach utilizes a meshfree generalized finite difference technique for spatial discretization within the Lagrangian framework and employs implicit time integration to develop both semi-implicit and fully implicit solvers for flow problems. Validation of the proposed approach is then appropriately examined through simulations of Couette and Poiseuille flows, achieving second-order accuracy with mean relative errors consistently maintained below 10−3. The findings indicate that while the fully implicit solver offers enhanced accuracy for the dynamic system, it incurs a considerable computational overhead of 30% compared to the semi-implicit solver in the flow problems. Therefore, the semi-implicit solver utilizing the Newmark time integration scheme is recommended as a judicious choice for the simulation of weakly compressible viscous flows, effectively balancing accuracy, efficiency, and numerical stability.

Keywords:

Implicit time integration

Lagrangian framework

Generalized finite difference method

Flow simulation

Semi-implicit solver

An Implicit Lagrangian Generalized Finite Difference Method for Flow Problems

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