## Cell vertex methods for inviscid and viscous flows.(English)Zbl 0779.76073

The cell vertex formulation of the finite volume method is now proving its worth for both the Navier-Stokes and Euler equations. We begin by reviewing the key advantages of the scheme for the Euler equations, and present some new algorithms for shock recovery and for modifying the update algorithm for cells crossed by recovered shocks. Applications will be shown for flow through a row of turbine blades. However, most attention is now focused on the use of the method for the Navier-Stokes equations. Typical results will be shown to demonstrate the capability of the method to model boundary layers accurately on coarse and distorted meshes, by showing detailed results on a variety of meshes. Error analysis for the method is based on setting the individual cell residuals to zero.

### MSC:

 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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### References:

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