A conservative, consistent, and scalable meshfree mimetic method

Understand

Mimetic methods discretize divergence by restricting the Gauss theorem to mesh cells.

• Because point clouds lack such geometric entities, construction of a compatible meshfree divergence remains a challenge.
• In this work, we define an abstract Meshfree Mimetic Divergence (MMD) operator on point clouds by contraction of field and virtual face moments.
• This MMD satisfies a discrete divergence theorem, provides a discrete local conservation principle, and is first-order accurate.