A Spatial-temporal Consistency Discretization Concept for Algebraic Volume-of-fluid Schemes on Arbitrary Meshes

Interfacial numerical diffusion at large Courant (Co) numbers is a well-known limitation of algebraic volume-of-fluid (VOF) schemes based on the normalized variable formulation (NVF). A critical inherent reason for this limitation is identified as the numerical inconsistency between the explicit spatial discretization of downwind weighting factors (DWF) and the Crank-Nicolson temporal discretization. A simple correction of the DWF expression, applicable to any NVF-based VOF method, is derived to suppress this diffusion, especially at high Co numbers. Using this correction, the widely studied compressive interface capturing scheme for arbitrary meshes (CICSAM) is refined into the CN-CICSAM scheme. Classical test cases, including the translation of a square/circle, the rotation of a slotted circle, the shear flow of a circle/sphere, the dam break, and the Rayleigh Taylor instability, validate the numerical refinements: the 1D translation case exhibits errors below 1×10-12 for all Co numbers, confirming the CN-CICSAM scheme’s complete compression ability; the CN-CICSAM scheme yields minimum errors among all tested schemes, typically 1/10-1/5 to those of the CICSAM scheme at large Co numbers. This study clarifies the spatial-temporal discretization inconsistency as an important source of numerical diffusion at high Co numbers, providing a foundational perspective for error suppression in interface-capturing schemes.