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Addendum to "Gauge Method for Viscous Incompressible Flows"

Weinan E, Jian-Guo Liu
2003 Communications in Mathematical Sciences  
The following paragraph should appear at the end of Section 1. Remark 1. Gauge transformation is a well-known concept in physics and has been used as a computational tool also. In fluid dynamics, Buttke was the first to use it as a computational tool to design vortex methods [1], following earlier work of Oseledets and others [3] . An alternative formulation was found by Maddocks and Pego [2] using the impetus-striction variables. This formulation does not seem to have the problem of numerical
more » ... oblem of numerical instability at the linear level. These authors are mainly concerned with writing down the Hamiltonian formulation of Euler's equation, whereas we are mainly concerned with using the gauge freedom to overcome the difficulties with boundary condition. REFERENCES [1] T. Buttke, Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible flows, in
doi:10.4310/cms.2003.v1.n4.a10 fatcat:sv67xturdjagzosqgyyslll7gu